Relevant bibliographies by topics / Algebras, linear – textbooks

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Algebras, linear – textbooks'

Author: Grafiati
Published: 29 July 2024
Last updated: 31 July 2024

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Journal articles on the topic "Algebras, linear – textbooks"

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Trefilova, E. S. "Изучение линейной алгебры на инженерных факультетах." Математический вестник Вятского государственного университета, no. 3(22) (December 24, 2021): 46–49. http://dx.doi.org/10.25730/vsu.0536.21.020.

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The proposed article discusses approaches to the study of linear algebra topics studied at the engineering faculties of Vyatka State University. The analysis of some textbooks and textbooks in mathematics for higher educational institutions has been carried out, as a result of which approaches in the sequence of studying some topics of linear algebra have been identified. The article suggests another sequence of studying topics based on the need for the appearance of a particular term. The advantages and disadvantages that appeared during the testing of such a sequence in the study of mathematics at the Faculty of electrical engineering are described. The article provides several examples of test questions to assess the level of assimilation of the material. The materials of the article can be useful for teachers working at engineering faculties. В предлагаемой статье рассмотрены подходы к изучению тем линейной алгебры, изучаемых на инженерных факультетах Вятского государственного университета. Проведен анализ некоторых учебников и учебных пособий по математике для высших учебных заведений, в результате которого выделены подходы в последовательности изучения некоторых тем линейной алгебры. В статье предложена еще одна последовательность изучения тем, основанная на необходимости появления того или иного термина. Описаны достоинства и недостатки, появившиеся в ходе апробации такой последовательности при изучении математики на электротехническом факультете. В статье приводятся несколько примеров тестовых вопросов, позволяющих оценить уровень усвоения материала. Материалы статьи могут быть полезны для преподавателей, работающих на инженерных факультетах.
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Yelovikova, Y. A. "Учебные пособия по алгебре для студентов младших курсов – разработка и опыт использования." Математический вестник Вятского государственного университета, no. 4(27) (September 14, 2023): 10–14. http://dx.doi.org/10.25730/vsu.0536.22.032.

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The ideas of developing textbooks on basic algebra courses are presented: "Fundamentals of General Algebra", "Theory of polynomials", "Linear Algebra". At the same time, one of the main tasks is to make the material as accessible as possible for students of the 1st and 2nd courses. Special attention is paid to the methodical processing of lecture material, its structuring, detailing. The methodology of working with the prepared textbooks is proposed, the experience of their practical use at the Department of Mathematical Analysis, Algebra and Geometry of Bryansk State University is analyzed. The authors of a series of textbooks hope that their development will help junior students adapt to new learning conditions, and teachers will successfully solve a number of methodological problems when teaching higher algebra. Излагаются идеи разработки учебных пособий по базовым курсам алгебры: «Основы общей алгебры», «Теория многочленов», «Линейная алгебра». При этом одна из основных задач – сделать материал максимально доступным для восприятия студентами 1-го и 2-го курсов. Особое внимание уделяется методической переработке лекционного материала, его структурированию, детализации. Предлагается методика работы с подготовленными учебными пособиями, анализируется опыт их практического использования на кафедре математического анализа, алгебры и геометрии Брянского государственного университета. Авторы серии учебных пособий надеются, что их разработка поможет студентам младших курсов адаптироваться к новым условиям обучения, а преподавателям – успешно решить ряд методических проблем при преподавании высшей алгебры.
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Zhang, Shengmei, Xiaowei Cai, and Jun Li. "Research on the Mixed Teaching Mode based on the New Form Textbook of Linear Algebra." Journal of Education and Educational Research 3, no. 3 (June 1, 2023): 41–44. http://dx.doi.org/10.54097/jeer.v3i3.9548.

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The new form of textbooks combines paper textbooks with new media resources, teaching with modern technology, and compensates for the content that paper textbooks cannot carry. The new form teaching materials of Linear algebra, including the integrated design of teaching content, strengthen the problem orientation, fully reflect the concepts of Flipped classroom, mixed teaching mode, inquiry learning, etc., improve the creativity, progressiveness and effectiveness of college mathematics teaching activities, and promote the benign development of college mathematics teaching.
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Siahaan, Meiva Marthaulina Lestari, and Fitriani. "Content Material of Vector Space for Development of Elementary Linear Algebra Module Integrated to Prezi." Plusminus: Jurnal Pendidikan Matematika 3, no. 3 (November 30, 2023): 425–40. http://dx.doi.org/10.31980/plusminus.v3i3.1506.

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Penelitian bertujuan untuk menganalisis materi muatan vektor yang kemudian digunakan untuk mengembangkan bahan ajar mata kuliah aljabar linier dasar materi muatan ruang vektor sehingga menghasilkan bahan ajar materi ruang vektor yang valid, praktis dan efektif. Metode penelitian yang digunakan adalah penelitian pengembangan Alessi dan Trollip dengan tiga tahap; perencanaan, desain dan pengembangan. Hasil penelitian ini adalah materi ruang vektor yang digunakan untuk mengembangkan bahan ajar adalah vektor pada R2, R3, dan Rn, persamaan parameter garis dan bidang, perkalian titik dan perkalian silang, serta persamaan koordinat garis dan bidang pada R3. Penilaian modul dari kedua ahli materi sebesar 3,33 artinya sangat layak, sedangkan dari kedua ahli media sebesar 3,9625 dengan kriteria sangat layak. Keunggulan produk ini adalah pertama, komposisi materi disusun berdasarkan analisis mendalam terhadap buku teks yang digunakan, sumber relevan, dan hasil ujian siswa masing-masing 3 tahun sebelumnya. Kedua, untuk memudahkan siswa dalam memahami materi ruang vektor karena disajikan gambar-gambar yang relevan dengan penjelasan dalam modul. Ketiga, materi dalam modul disajikan dengan media Prezi terintegrasi berupa PowerPoint sehingga dapat menarik perhatian siswa dan membuat siswa fokus pada materi. The research has purpose to analyze vector content material which is then used to develop teaching materials for elementary linear algebra courses on vector space content material so as to produce teaching materials on vector space material that are valid, practical and effective. The research method used is Alessi and Trollip development research with three stages; planning, design and development. The results of this research are the vector space materials used for developing teaching materials are vectors in R2, R3, and Rn, line and plane parameter equations, dot products and cross products, yet line and plane coordinate equations in R3. The module assessment from the two material experts was 3.33, which means very feasible, while from the two media experts it was 3.9625 with very feasible criteria. The benefits of this product are first, the composition of the material is prepared based on in-depth analysis of the textbooks used, relevant sources, and student test results in the previous 3 years respectively. Second, to make it easier for students to understand vector space material because images are presented that are relevant to the explanation in the module. Third, the material in the module is presented with integrated Prezi media in the form of PowerPoint so that it can attract students' attention and make students focus on the material.
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Kesumawati, Nila, Nyiayu Fahriza Fuadiah, Lusiana Lusiana, and Dina Octaria. "Teaching Materials for Algebra and Linear Programs Based on Pancasila Student Profiles." Jurnal Riset Pendidikan Matematika 10, no. 1 (May 31, 2023). http://dx.doi.org/10.21831/jrpm.v10i1.55392.

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The aims of this study were: 1) to develop textbooks based on Pancasila student profiles for Algebra and Linear Programming courses; and 2) developing instruments to measure the achievement of the dimensions of the Pancasila student profile. The quality of the products developed is assessed based on: 1) validity aspects, 2) practical aspects, and 3) effectiveness aspects of students' mathematical creative and critical thinking abilities. The research method used is the ADDIE Research and Development (R D) model. The research subjects were 19 students in the first semester of the Mathematics Education Study Program. The instruments used to obtain the quality of the textbooks developed were: 1) textbook assessment sheets to measure validity, 2) response questionnaires and observation sheets to measure practicality, 3) critical thinking skills and mathematical creative questions to measure effectiveness. The validity quality of textbooks fulfilling the valid criteria is shown by the average score of 3.53 out of a maximum score of 4 which means that it is very valid for practicality quality to get an average score of 3.32 out of a maximum score of 4 which means practical, quality of effectiveness in terms of critical thinking skills and creative mathematical students who meet the affective criteria are shown, namely 58% which means sufficient and the average score for critical and creative thinking skills is 67.27 which means quite effective. Textbooks and RPS are suitable for use in lectures
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Castro-Rodríguez, Elena, Angeliki Mali, and Vilma Mesa. "University students’ engagement with digital mathematics textbooks: a case of linear algebra." International Journal of Mathematical Education in Science and Technology, December 11, 2022, 1–23. http://dx.doi.org/10.1080/0020739x.2022.2147104.

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Gerami, Saba, Eric Khiu, Vilma Mesa, and Thomas Judson. "Conceptions of span in linear algebra: from textbook examples to student responses." Educational Studies in Mathematics, March 4, 2024. http://dx.doi.org/10.1007/s10649-024-10306-8.

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Dubovyk, Vitalii. "PECULIARITIES OF THE STRUCTURE AND METHODOLOGICAL ASPECTS OF USING THE ELECTRONIC TEXTBOOKS DURING THE LEARNING OF LINEAR ALGEBRA OF STUDENTS OF PEDAGOGICAL UNIVERSITIES." Academic Notes Series Pedagogical Science 1, no. 198 (December 2021). http://dx.doi.org/10.36550/2415-7988-2021-1-198-235-238.

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Dissertations / Theses on the topic "Algebras, linear – textbooks"

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Grande, André Lúcio. "O conceito de independência e dependência linear e os registros de representação semiótica nos livros didáticos de Álgebra Linear." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11123.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
This research aims to investigate which semiotic representation registers are most used in Linear Algebra textbooks in the presentation and study of the topic linear independence. The mathematics textbook is a resource much used by the teachers in its work. They present many representation registers, which can to be analyzed qualitatively to assess their potential contribution to the teaching-learning process. To this end, five Linear Algebra textbooks were selected for an analysis which involved the diagnosis of the representation registers used in the definition of linear independence, as well as the examples and exercises proposed for its study. The theory used in the analysis of these textbooks was Raymond Duval´s theory of Registers of Semiotic Representation, which highlights the importance of changes between registers in the learning of mathematical objects. In each textbooks, the registers present were classified and analyzed, along with the possible transformations of registers as carried out in the resolution of the examples and considered exercises. As result, scarcity of the use of some registers of representation it was evidenced in the chapters that approach the slight knowledge of independence and linear dependence, as for example, the geometric one to determine if a set of vectors is linearly independent or not, and the register of the natural language, in the resolution of examples and considered exercises that involve demonstrations. The analysis also indicated a lack of attention to conversions between registers in the examples and proposed exercises of analyzed textbooks
Esta pesquisa tem como objetivo investigar nos livros didáticos de Álgebra Linear quais são os registros de representação semiótica mais utilizados no estudo das noções e atividades propostas sobre independência linear. O livro didático é um recurso muito utilizado pelos professores no seu trabalho, o qual apresenta muitos registros de representação que podem ser analisados qualitativamente para a contribuição no processo de ensino-aprendizagem. Para isso, foram selecionados cinco livros didáticos de Álgebra Linear que se diagnosticou os registros de representação utilizados na definição, exemplos e exercícios propostos a respeito de independência linear. A teoria utilizada na análise dos livros didáticos foi a dos Registros de Representação Semiótica de Raymond Duval, que destaca a importância da mudança de registros na aprendizagem dos objetos matemáticos. Em cada obra, os registros foram classificados e analisados, bem como as possíveis transformações de registros realizadas na resolução dos exemplos e exercícios propostos. Como resultado, constatou-se nos capítulos que abordam as noções de independência e dependência linear uma escassez da utilização de alguns registros de representação, como por exemplo, o geométrico para determinar se um conjunto de vetores é linearmente independente ou não, e o registro da língua natural, na resolução de exemplos e exercícios propostos que envolvem demonstrações. Além disso, verificou-se a falta de conversão de registros nas definições, exemplos e exercícios propostos dos livros didáticos analisados
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Karrer, Monica. "Articulação entre Álgebra Linear e Geometria - Um Estudo sobre as Transformações Lineares na Perspectiva dos Registros de Representação Semiótica." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11068.

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Pontificia Universidade de São Paulo
This study addressed questions related to the teaching and learning of Linear Algebra in Higher Education. More precisely, it involved the design of activities which concerned the mathematical object linear transformations and which engaged learners in exploring the conversion of registers in a dynamic geometry environment. The aim was to investigate the learning trajectories of university students and the impact of the didactical choices which characterized the teaching approach. The study was organized into two phases. In the first, preliminary studies along with theoretical considerations led to the formulation of hypotheses and to the identification of the conceptual tools to be used in the analysis of the learning trajectories. Using as a theoretical framework Duval s theory of semiotic representation registers (1995, 2000, 2003), during this phase the registers and conversions present in sections on linear transformations in both Linear Algebra and Computational Graphics textbooks were analyzed. In addition, eighty-six students of Computer Science completed a questionnaire about linear transformation. These studies highlighted difficulties in relation to the exploration of different semiotic registers on the part of the students, particularly as concerned matrixial and graphical registers. In the second phase, which employed the methodology of Design Experiments (COBB et al., 2003), activities were developed to explore the diverse representation of planar linear transformations using Cabri-Géomètre and paper&pencil environments. Six students of Computational Engineering at a private university in the city of São Paulo participated in the experiment. The results indicated evolutions in the subjects understandings of the conditions for determinating linear transformations and of the particularities of their graphs, as well as a more comprehensive mastery of diverse representations and conversions. Analysis of students trajectories also revealed how students strategies were mediated by characteristics of the tasks and the computational environment.
Este estudo trata de questões relativas ao ensino e à aprendizagem de conceitos da Álgebra Linear no ensino superior. Mais precisamente, esta pesquisa envolveu o design de atividades sobre o objeto matemático transformação linear , explorando a conversão de registros em um ambiente de geometria dinâmica. Com isso buscou-se investigar as trajetórias de aprendizagem de estudantes universitários e o impacto dessas escolhas na abordagem de ensino. O trabalho foi organizado em duas fases. Na primeira, realizaram-se estudos preliminares e desenvolvimentos teóricos para a formulação de hipóteses de trabalho e identificação de ferramentas conceituais para a análise das trajetórias. Com base na teoria dos registros de representação semiótica de DUVAL (1995, 2000, 2003), analisou-se a exploração dos registros e conversões presentes no conteúdo das transformações, tanto nos livros didáticos de Álgebra Linear quanto nos de Computação Gráfica. Ainda, aplicou-se um questionário sobre transformações lineares a oitenta e seis (86) estudantes da área de Computação. Estes estudos apontaram deficiências e dificuldades com relação à exploração de diferentes registros por parte dos estudantes, principalmente os registros matricial e gráfico. Na segunda fase, com base na metodologia de Design Experiments (COBB et al., 2003), foram concebidas atividades de exploração das diversas representações de transformações lineares planas, nos ambientes Cabri-Géomètre e papel&lápis. Seis (6) estudantes do curso de Engenharia da Computação de uma instituição particular de ensino superior da cidade de São Paulo participaram do experimento. Os resultados revelaram evoluções dos sujeitos na compreensão das condições de determinação de transformações lineares e de particularidades gráficas inerentes a estas, além de um domínio mais amplo das diversas representações e de suas conversões. Por fim, foram observados efeitos específicos nas estratégias dos estudantes relacionados às características das tarefas e do ambiente computacional.
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Oliveira, Silvio Barbosa de. "As equações diofantinas lineares e o livro didático de matemática para o ensino médio." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11059.

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This work involves a qualitative study of how the theme of linear Diophantine equations is approached in mathematics textbooks for high school students. Using the methods associated with content analysis (Bardin, 1977), I search for references, in both explicit and implicit forms, to these equations in two different sets of high school mathematics textbooks, both of which had been approved in the last PNLEM (a national project for the assessment of high school textbooks). Although elementary number theory has been highlighted by researchers in mathematics education, such as Campbell and Zazkis (2002), as a subject apt for the introduction and development of fundamental mathematical ideas in compulsory education, the results of this investigation indicate that it receives little attention in the textbooks analysed
Neste trabalho apresento um estudo qualitativo sobre a abordagem dada pelo livro didático do Ensino Médio ao tema equações diofantinas lineares . Por meio de uma análise de conteúdo, segundo Bardin (1977), busquei o assunto em sua forma explícita e implícita em duas coleções de Matemática para o Ensino Médio, aprovadas no último PNLEM. Embora a Teoria Elementar dos Números venha sendo tratada por pesquisadores de Educação Matemática, como Campbell e Zazkis (2002), como assunto propício para a introdução e desenvolvimento de idéias matemáticas fundamentais, no Ensino Básico, os resultados desta investigação indicam a pouca exploração do assunto por parte das coleções analisadas
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Ulrychová, Eva. "Lineární algebra na školách netechnického směru." Doctoral thesis, 2013. http://www.nusl.cz/ntk/nusl-327878.

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The thesis consists of two equal parts - of a part dealing with didactic aspects of teaching linear algebra, and of an unconventionally approached textbook Fundamentals of Linear Algebra, which is appended as a separate attachment. The didactic part deals with teaching mathematics, especially linear algebra, at the University of Economics in Prague, namely from the historical and methodological point of view. The thesis also includes a detailed evaluation of students' knowledge tests. The conclusions are largely portable to other non- technically oriented universities. The textbook is designed with respect to two levels of difficulty; it is written in the form accessible for students with lighter assumptions for the study of mathematics. The textbook is designed especially for students of universities where mathematics is not the main focus; it may also serve to interested high schools students as an introduction to a more advanced study of linear algebra.
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Books on the topic "Algebras, linear – textbooks"

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Penney, Richard C. Linear algebra: Ideas and applications. New York: J. Wiley, 1998.

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A, Beauregard Raymond, and Katz Victor J, eds. Linear algebra. 3rd ed. Reading, Mass: Addison-Wesley, 1995.

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A, Beauregard Raymond, and Katz Victor J, eds. Linear algebra. 2nd ed. Reading, Massachusetts: Addison-Wesley Publishing Co., 1990.

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A, Beauregard Raymond, ed. Linear algebra. Reading, Mass: Addison-Wesley, 1987.

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B, Fraleigh John. Linear algebra. 2nd ed. Reading, Massachusetts: Addison-Wesley Publishing Co., 1990.

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Bretscher, Otto. Linear algebra with applications. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2001.

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Bretscher, Otto. Linear algebra with applications. 4th ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2009.

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Bretscher, Otto. Linear algebra with applications. Upper Saddle River, N.J: Prentice Hall, 1997.

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W, Johnson Lee, Riess R. Dean 1940-, and Arnold Jimmy T. 1941-, eds. Introduction to linear algebra. 5th ed. Boston: Addison-Wesley, 2002.

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1940-, Riess R. Dean, and Arnold Jimmy T. 1941-, eds. Introduction to linear algebra. 4th ed. Reading Mass: Addison-Wesley, 1997.

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Book chapters on the topic "Algebras, linear – textbooks"

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Chen, Xiaoyu, Haotian Shuai, Dongming Wang, and Jing Yang. ": A Linear Algebra Textbook System." In Artificial Intelligence and Symbolic Computation, 209–14. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99957-9_14.

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Cook, John Paul, Dov Zazkis, and Adam Estrup. "Rationale for Matrix Multiplication in Linear Algebra Textbooks." In Challenges and Strategies in Teaching Linear Algebra, 103–25. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-66811-6_5.

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Jacob, Bill. "Key Concepts of Linear Algebra in Rn." In Textbooks in Mathematical Sciences, 155–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-59277-5_5.

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Pillonetto, Gianluigi, Tianshi Chen, Alessandro Chiuso, Giuseppe De Nicolao, and Lennart Ljung. "Regularization of Linear Regression Models." In Regularized System Identification, 33–93. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95860-2_3.

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AbstractLinear regression models are widely used in statistics, machine learning and system identification. They allow to face many important problems, are easy to fit and enjoy simple analytical properties. The simplest method to fit linear regression models is least squares whose systematic treatment is available in many textbooks, e.g., [35, Chap. 4], [12]. Linear regression models can be fitted also in different way and a class of methods that we will consider in this chapter is the so-called regularized least squares. It is an extension of least squares which minimizes the sum of the square loss function and a regularization term. This latter can take various forms, leading to several variants which have been applied extensively in theory as well as in practical applications. In this chapter, we will focus on these methods and introduce their fundamentals. In the first part of the appendix to this chapter, we also report some basic results of linear algebra useful for the reading.
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Helemskii, A. YA. "Foundations." In Banach and Locally Convex Algebras, 1–55. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198535782.003.0001.

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Abstract Strictly speaking, we shall only start on the subject of this book after we have introduced an additional structure – multiplication — into the objects of linear functional analysis — Banach spaces and some more general spaces; this is precisely what we shall talk about in the first definition of the first chapter. But first, in Chapter 0, it is necessary to indicate the stock of background material which is important: for us as a foundation. Some of this material is widely known and is contained in standard textbooks but there is some which can be found only in specialized monographs and articles in journals. Therefore the amount of detail given in different: places in this chapter is very varied.
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"D. Linear Algebra Summary." In AMS/MAA Textbooks, 503–8. Providence, Rhode Island: American Mathematical Society, 2015. http://dx.doi.org/10.1090/text/026/15.

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Pretzel, Oliver. "Appendix LA Linear algebra." In Error-Correcting Codes and Finite Fields, 79–93. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198596783.003.0006.

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Abstract This appendix gives a sketch of that part of linear algebra that is required for coding theory. The appendix is not intended to be a learning text and the reader who is completely unfamiliar with the subject should study one of the textbooks Birkhoff and MacLane (1977), Cohn (1982), Noble and Daniel (1977) or Strang (1980) before tackling coding theory.
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"Appendix I, Linear algebra facts." In AMS/MAA Textbooks, 141–44. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/text/013/07.

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Rice, Adrian. "Algebra." In The Mathematical World of Charles L. Dodgson (Lewis Carroll), 57–86. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198817000.003.0003.

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This chapter is concerned with a single textbook written by Dodgson in 1867—An Elementary Treatise on Determinants. His book concerned the study of determinants, an algebraic construct that had come to the fore during the 19th century, and presented a new method, called the method of condensation, for evaluating them; this method was due to Dodgson and was the subject of his only refereed journal paper. The book also applied his results to the solution of simultaneous linear equations, and included the proof of a theorem describing when a system of linear equations is consistent. The book’s impact and influence are discussed in the concluding section of this chapter.
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10

Kaye, Phillip, Raymond Laflamme, and Michele Mosca. "Linear Algebra and the Dirac Notation." In An Introduction to Quantum Computing. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198570004.003.0005.

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We assume the reader has a strong background in elementary linear algebra. In this section we familiarize the reader with the algebraic notation used in quantum mechanics, remind the reader of some basic facts about complex vector spaces, and introduce some notions that might not have been covered in an elementary linear algebra course. The linear algebra notation used in quantum computing will likely be familiar to the student of physics, but may be alien to a student of mathematics or computer science. It is the Dirac notation, which was invented by Paul Dirac and which is used often in quantum mechanics. In mathematics and physics textbooks, vectors are often distinguished from scalars by writing an arrow over the identifying symbol: e.g a⃗. Sometimes boldface is used for this purpose: e.g. a. In the Dirac notation, the symbol identifying a vector is written inside a ‘ket’, and looks like |a⟩. We denote the dual vector for a (defined later) with a ‘bra’, written as ⟨a|. Then inner products will be written as ‘bra-kets’ (e.g. ⟨a|b⟩). We now carefully review the definitions of the main algebraic objects of interest, using the Dirac notation. The vector spaces we consider will be over the complex numbers, and are finite-dimensional, which significantly simplifies the mathematics we need. Such vector spaces are members of a class of vector spaces called Hilbert spaces. Nothing substantial is gained at this point by defining rigorously what a Hilbert space is, but virtually all the quantum computing literature refers to a finite-dimensional complex vector space by the name ‘Hilbert space’, and so we will follow this convention. We will use H to denote such a space. Since H is finite-dimensional, we can choose a basis and alternatively represent vectors (kets) in this basis as finite column vectors, and represent operators with finite matrices. As you see in Section 3, the Hilbert spaces of interest for quantum computing will typically have dimension 2n, for some positive integer n. This is because, as with classical information, we will construct larger state spaces by concatenating a string of smaller systems, usually of size two.
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