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Journal articles on the topic 'Real rank'

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Author: Grafiati
Published: 10 March 2023

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1

Beasley, LeRoy B., and Thomas J. Laffey. "Real rank versus nonnegative rank." Linear Algebra and its Applications 431, no. 12 (December 2009): 2330–35. http://dx.doi.org/10.1016/j.laa.2009.02.034.

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2

Ballico, Edoardo, and Alessandra Bernardi. "Real and Complex Rank for Real Symmetric Tensors with Low Ranks." Algebra 2013 (March 21, 2013): 1–5. http://dx.doi.org/10.1155/2013/794054.

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We study the case of a real homogeneous polynomial whose minimal real and complex decompositions in terms of powers of linear forms are different. We prove that if the sum of the complex and the real ranks of is at most , then the difference of the two decompositions is completely determined either on a line or on a conic or two disjoint lines.
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3

Seigal, Anna, and Bernd Sturmfels. "Real rank two geometry." Journal of Algebra 484 (August 2017): 310–33. http://dx.doi.org/10.1016/j.jalgebra.2017.04.014.

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4

Banchi, Maurizio. "Rank and border rank of real ternary cubics." Bollettino dell'Unione Matematica Italiana 8, no. 1 (July 21, 2015): 65–80. http://dx.doi.org/10.1007/s40574-015-0027-z.

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5

Ballico, E. "An upper bound for the real tensor rank and the real symmetric tensor rank in terms of the complex ranks." Linear and Multilinear Algebra 62, no. 11 (September 24, 2013): 1546–52. http://dx.doi.org/10.1080/03081087.2013.839671.

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6

Jeong, J. A., G. H. Park, and D. Y. Shin. "Stable rank and real rank of graph C∗-algebras." Pacific Journal of Mathematics 200, no. 2 (October 1, 2001): 331–43. http://dx.doi.org/10.2140/pjm.2001.200.331.

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7

Sims, Aidan, David Pask, and Adam Sierakowski. "Real rank and topological dimension of higher rank graph algebras." Indiana University Mathematics Journal 66, no. 6 (2017): 2137–68. http://dx.doi.org/10.1512/iumj.2017.66.6212.

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8

Chu, Moody T., and Robert J. Plemmons. "Real-Valued, Low Rank, Circulant Approximation." SIAM Journal on Matrix Analysis and Applications 24, no. 3 (January 2003): 645–59. http://dx.doi.org/10.1137/s0895479801383166.

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9

Chigogidze, A., and V. Valov. "C*-algebras of infinite real rank." Bulletin of the Australian Mathematical Society 66, no. 3 (December 2002): 487–96. http://dx.doi.org/10.1017/s0004972700040326.

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We introduce the notion of weakly (strongly) infinite real rank for unital C*-algebras. It is shown that a compact space X is weakly (strongly) infine-dimensional if and only if C (X) has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group C*-algebra C* (∞) of the free group on countable number of generators has strongly infinite real rank.
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10

Blekherman, Grigoriy, and Rainer Sinn. "Real rank with respect to varieties." Linear Algebra and its Applications 505 (September 2016): 344–60. http://dx.doi.org/10.1016/j.laa.2016.04.035.

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11

Brown, Lawrence G., and Gert K. Pedersen. "C∗-algebras of real rank zero." Journal of Functional Analysis 99, no. 1 (July 1991): 131–49. http://dx.doi.org/10.1016/0022-1236(91)90056-b.

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12

Michałek, Mateusz, Hyunsuk Moon, Bernd Sturmfels, and Emanuele Ventura. "Real rank geometry of ternary forms." Annali di Matematica Pura ed Applicata (1923 -) 196, no. 3 (August 23, 2016): 1025–54. http://dx.doi.org/10.1007/s10231-016-0606-3.

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13

Carlini, Enrico, Mario Kummer, Alessandro Oneto, and Emanuele Ventura. "On the real rank of monomials." Mathematische Zeitschrift 286, no. 1-2 (October 21, 2016): 571–77. http://dx.doi.org/10.1007/s00209-016-1774-y.

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14

Mo, M. Y. "Rank 1 real Wishart spiked model." Communications on Pure and Applied Mathematics 65, no. 11 (August 6, 2012): 1528–638. http://dx.doi.org/10.1002/cpa.21415.

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15

Archbold, Robert J., and Eberhard Kaniuth. "Stable rank and real rank of compact transformation group C*-algebras." Studia Mathematica 175, no. 2 (2006): 103–20. http://dx.doi.org/10.4064/sm175-2-1.

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16

KAWAZOE, Takeshi. "Real Hardy spaces on real rank 1 semisimple Lie groups." Japanese journal of mathematics. New series 31, no. 2 (2005): 281–343. http://dx.doi.org/10.4099/math1924.31.281.

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17

Sudo, Takahiro. "A CLASSIFICATION OF C*-ALGEBRAS BY K-THEORY RANK AND REAL RANK." Far East Journal of Mathematical Sciences (FJMS) 134 (February 2, 2022): 1–11. http://dx.doi.org/10.17654/0972087122001.

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18

Conley, Charles H., and Martin Westerholt-Raum. "Harmonic Maaß–Jacobi forms of degree 1 with higher rank indices." International Journal of Number Theory 12, no. 07 (September 6, 2016): 1871–97. http://dx.doi.org/10.1142/s1793042116501165.

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We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of order 4. In ranks exceeding 1, the notions of H-harmonicity and semi-holomorphicity are the same.
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19

Al-Akashi, Falah Hassan Ali, and Diana Inkpen. "A Scalable Real-Time Agent-Based Information Retrieval Engine." International Journal of Software Innovation 10, no. 1 (January 2022): 1–14. http://dx.doi.org/10.4018/ijsi.292022.

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In distributed information retrieval systems, information in web should be ranked based on a combination of multiple features. Linear combination of ranks has been the dominant approach due to its simplicity and efficiency. Such a combination scheme in distributed infrastructure requires that ranks in resources or agents are comparable to each other. The main challenge is how to transform the raw rank values of different criteria appropriately to make them comparable before any combination. In this manuscript, we will demonstrate how to rank Web documents based on its resource-provided information stream and how to combine and incorporate several raking schemas in one time. The system was tested on the queries provided by a Text Retrieval Conference (TREC), and our experimental results showed that it is robust and efficient compared with similar platforms that used offline data resources.
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20

Bratteli, Ola, and George Elliott. "Small eigenvalue variation and real rank zero." Pacific Journal of Mathematics 175, no. 1 (September 1, 1996): 47–59. http://dx.doi.org/10.2140/pjm.1996.175.47.

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21

Ondrus, Alex. "Minimal anisotropic groups of higher real rank." Michigan Mathematical Journal 60, no. 2 (July 2011): 355–97. http://dx.doi.org/10.1307/mmj/1310667981.

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22

Lin, Huaxin. "Simple $AH$-algebras of real rank zero." Proceedings of the American Mathematical Society 131, no. 12 (December 1, 2003): 3813–19. http://dx.doi.org/10.1090/s0002-9939-03-06995-8.

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23

CHIGOGIDZE, ALEX. "UNIVERSAL C*-ALGEBRA OF REAL RANK ZERO." Infinite Dimensional Analysis, Quantum Probability and Related Topics 03, no. 03 (September 2000): 445–52. http://dx.doi.org/10.1142/s0219025700000248.

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It is well known that every commutative separable unital C*-algebra of real rank zero is a quotient of the C*-algebra of all compex continuous functions defined on the Cantor cube. We prove a non-commutative version of this result by showing that the class of all separable unital C*-algebras of real rank zero coincides with the class of quotients of a certain separable unital C*-algebra of real rank zero.
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24

Kazakov, Matthew, David W. Kribs, and Rajesh Pereira. "Real higher rank numerical ranges and ellipsoids." Linear Algebra and its Applications 577 (September 2019): 204–13. http://dx.doi.org/10.1016/j.laa.2019.04.028.

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25

Miatello, R., and N. R. Wallach. "Kuznetsov formulas for real rank one groups." Journal of Functional Analysis 93, no. 1 (October 1990): 171–206. http://dx.doi.org/10.1016/0022-1236(90)90138-b.

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26

Ventura, Emanuele. "Real rank boundaries and loci of forms." Linear and Multilinear Algebra 67, no. 7 (March 20, 2018): 1404–19. http://dx.doi.org/10.1080/03081087.2018.1454395.

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27

Sudo, Takahiro. "The Real Rank of CCR C*-Algebra." Kyungpook mathematical journal 48, no. 2 (June 30, 2008): 223–32. http://dx.doi.org/10.5666/kmj.2008.48.2.223.

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28

Hou, Dennis. "On hypercomplexifying real forms of arbitrary rank." Advances in Applied Clifford Algebras 11, no. 2 (December 2001): 265–71. http://dx.doi.org/10.1007/bf03042316.

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29

Jeong, Ja A., and Gi Hyun Park. "Graph C*-Algebras with Real Rank Zero." Journal of Functional Analysis 188, no. 1 (January 2002): 216–26. http://dx.doi.org/10.1006/jfan.2001.3830.

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30

Rubei, Elena. "Generalization of real interval matrices to other fields." Electronic Journal of Linear Algebra 35 (February 1, 2019): 285–96. http://dx.doi.org/10.13001/1081-3810.3953.

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An interval matrix is a matrix whose entries are intervals in $\R$. This concept, which has been broadly studied, is generalized to other fields. Precisely, a rational interval matrix is defined to be a matrix whose entries are intervals in $\Q$. It is proved that a (real) interval $p \times q$ matrix with the endpoints of all its entries in $\Q$ contains a rank-one matrix if and only if it contains a rational rank-one matrix, and contains a matrix with rank smaller than $\min\{p,q\}$ if and only if it contains a rational matrix with rank smaller than $\min\{p,q\}$; from these results and from the analogous criterions for (real) inerval matrices, a criterion to see when a rational interval matrix contains a rank-one matrix and a criterion to see when it is full-rank, that is, all the matrices it contains are full-rank, are deduced immediately. Moreover, given a field $K$ and a matrix $\al$ whose entries are subsets of $K$, a criterion to find the maximal rank of a matrix contained in $\al$ is described.
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31

Archbold, Robert J., and Eberhard Kaniuth. "Stable rank and real rank for some classes of group $C^\ast $-algebras." Transactions of the American Mathematical Society 357, no. 6 (January 21, 2005): 2165–86. http://dx.doi.org/10.1090/s0002-9947-05-03835-3.

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32

Chouh, Meriem, Mohamed Hanafi, and Kamel Boukhetala. "Semi-nonnegative rank for real matrices and its connection to the usual rank." Linear Algebra and its Applications 466 (February 2015): 27–37. http://dx.doi.org/10.1016/j.laa.2014.09.046.

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33

Elsenhans, Andreas-Stephan, and Jörg Jahnel. "Examples of surfaces with real multiplication." LMS Journal of Computation and Mathematics 17, A (2014): 14–35. http://dx.doi.org/10.1112/s1461157014000199.

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AbstractWe construct explicit $K3$ surfaces over $\mathbb{Q}$ having real multiplication. Our examples are of geometric Picard rank 16. The standard method for the computation of the Picard rank provably fails for the surfaces constructed.
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34

Goodman, Roe. "Whittaker transforms on real-rank one Lie groups." Colloquium Mathematicum 60, no. 1 (1990): 99–128. http://dx.doi.org/10.4064/cm-60-61-1-99-128.

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35

Kodaka, Kazunori, and Hiroyuki Osaka. "Real Rank of Tensor Products of C ∗ -Algebras." Proceedings of the American Mathematical Society 123, no. 7 (July 1995): 2213. http://dx.doi.org/10.2307/2160959.

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36

Li, Dehe, and Shujie Zhai. "Real Hypersurfaces in Complex Grassmannians of Rank Two." Mathematics 9, no. 24 (December 14, 2021): 3238. http://dx.doi.org/10.3390/math9243238.

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It is known that there does not exist any Hopf hypersurface in complex Grassmannians of rank two of complex dimension 2m with constant sectional curvature for m≥3. The purpose of this article is to extend the above result, and without the Hopf condition, we prove that there does not exist any locally conformally flat real hypersurface for m≥3.
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37

Blackadar, B., M. Dadarlat, and M. Rordam. "The real rank of inductive limit $C^*$-algebras." MATHEMATICA SCANDINAVICA 69 (December 1, 1991): 211. http://dx.doi.org/10.7146/math.scand.a-12379.

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38

Ji, Shanyu. "Algebraicity of real analytic hypersurfaces with maximal rank." American Journal of Mathematics 124, no. 6 (2002): 1083–102. http://dx.doi.org/10.1353/ajm.2002.0039.

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39

Fang, Xiaochun. "The real rank zero property of crossed product." Proceedings of the American Mathematical Society 134, no. 10 (May 8, 2006): 3015–24. http://dx.doi.org/10.1090/s0002-9939-06-08357-2.

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40

Fourie, J. H., G. J. Groenewald, D. B. Janse van Rensburg, and A. C. M. Ran. "Rank one perturbations of H -positive real matrices." Linear Algebra and its Applications 439, no. 3 (August 2013): 653–74. http://dx.doi.org/10.1016/j.laa.2013.04.010.

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41

Ballico, Edoardo. "On the typical rank of real bivariate polynomials." Linear Algebra and its Applications 452 (July 2014): 263–69. http://dx.doi.org/10.1016/j.laa.2014.04.001.

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42

Petrović, Zoran Z. "Spaces of real matrices of fixed small rank." Linear Algebra and its Applications 431, no. 8 (September 2009): 1199–207. http://dx.doi.org/10.1016/j.laa.2009.04.012.

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43

Lam, Kee Yuen, and Paul Yiu. "Linear spaces of real matrices of constant rank." Linear Algebra and its Applications 195 (December 1993): 69–79. http://dx.doi.org/10.1016/0024-3795(93)90257-o.

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44

Comon, Pierre, and Giorgio Ottaviani. "On the typical rank of real binary forms." Linear and Multilinear Algebra 60, no. 6 (June 2012): 657–67. http://dx.doi.org/10.1080/03081087.2011.624097.

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45

Jeong, Ja A. "Real rank of C*-algebras associated with graphs." Journal of the Australian Mathematical Society 77, no. 1 (August 2004): 141–47. http://dx.doi.org/10.1017/s1446788700010211.

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AbstractFor a locally finite directed graph E, it is known that the graph C*-algebra C*(E) has real rank zero if and only if the graph E satisfies the loop condition (K). In this paper we extend this to an arbitrary directed graph case using the desingularization of a graph due to Drinen and Tomforde
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46

Lin, Huaxin. "Type I $C^*$-algebras of real rank zero." Proceedings of the American Mathematical Society 125, no. 9 (1997): 2671–76. http://dx.doi.org/10.1090/s0002-9939-97-03890-2.

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47

LIN, HUAXIN. "EXTENSIONS BY C*-ALGEBRAS WITH REAL RANK ZERO." International Journal of Mathematics 04, no. 02 (April 1993): 231–52. http://dx.doi.org/10.1142/s0129167x93000133.

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We show that all trivial (unital and essential) extensions of C (X) by a σ-unital purely infinite simple C*-algebra A with K1(A) = 0 are unitarily equivalent, provided that X is homeomorphic to a compact subset of the real line or the unit circle. Therefore all (unital and essential) extensions of such can be completely determined by Ext(B, A). An invariant is introduced to classify all such trivial (unital and essential) extensions of C (X) by a σ-unital C*-algebra A with the properties that RR (M (A)) = 0 and C (A) is simple.
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48

Rees, Elmer G. "Linear spaces of real matrices of large rank." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 126, no. 1 (1996): 147–51. http://dx.doi.org/10.1017/s030821050003064x.

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For every k1 0 < k < m ≧ n, there are linear spaces of real n × m matrices which have dimension (m − k)(n − k) and every nonzero element has rank greater than k. Examples of such spaces are constructed and conditions are given under which they have the largest possible dimension.
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49

Erbay, Hasan. "Subspace tracking in low-rank real-time systems." Applied Mathematics and Computation 173, no. 2 (February 2006): 1300–1309. http://dx.doi.org/10.1016/j.amc.2005.04.072.

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50

Dadarlat, Marius, and Terry A. Loring. "Extensions of certain real rank zero $C^*$-algebras." Annales de l’institut Fourier 44, no. 3 (1994): 907–25. http://dx.doi.org/10.5802/aif.1420.

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