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Journal articles on the topic 'Matrix coefficients'

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Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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1

Kholkin, A. M., and F. S. Rofe-Beketov. "On Spectrum of Differential Operator with Block-Triangular Matrix Coefficients." Zurnal matematiceskoj fiziki, analiza, geometrii 10, no. 1 (March 25, 2014): 44–63. http://dx.doi.org/10.15407/mag10.01.044.

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2

Gollwitzer, Herman. "Matrix Patterns and Undetermined Coefficients." College Mathematics Journal 25, no. 5 (November 1994): 444. http://dx.doi.org/10.2307/2687511.

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3

Gollwitzer, Herman. "Matrix Patterns and Undetermined Coefficients." College Mathematics Journal 25, no. 5 (November 1994): 444–48. http://dx.doi.org/10.1080/07468342.1994.11973650.

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4

Szpruch, Dani. "On Shahidi local coefficients matrix." manuscripta mathematica 159, no. 1-2 (July 7, 2018): 117–59. http://dx.doi.org/10.1007/s00229-018-1052-x.

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5

Sun, Binyong. "Matrix coefficients of cohomologically induced representations." Compositio Mathematica 143, no. 01 (January 2007): 201–21. http://dx.doi.org/10.1112/s0010437x06002508.

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6

Arteaga, Oriol, Enric Garcia-Caurel, and Razvigor Ossikovski. "Anisotropy coefficients of a Mueller matrix." Journal of the Optical Society of America A 28, no. 4 (March 11, 2011): 548. http://dx.doi.org/10.1364/josaa.28.000548.

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7

Steenge, Albert E., and Rachel C. Reyes. "Return of the capital coefficients matrix." Economic Systems Research 32, no. 4 (February 28, 2020): 439–50. http://dx.doi.org/10.1080/09535314.2020.1731682.

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8

Heijungs, Reinout. "Sensitivity coefficients for matrix-based LCA." International Journal of Life Cycle Assessment 15, no. 5 (February 20, 2010): 511–20. http://dx.doi.org/10.1007/s11367-010-0158-5.

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9

Duran, Antonio J., and Mourad E. H. Ismail. "Differential coefficients of orthogonal matrix polynomials." Journal of Computational and Applied Mathematics 190, no. 1-2 (June 2006): 424–36. http://dx.doi.org/10.1016/j.cam.2005.02.019.

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10

Apfeldorf, Karyn M. "Multi-matrix models from jet coefficients." Nuclear Physics B 360, no. 2-3 (August 1991): 480–506. http://dx.doi.org/10.1016/0550-3213(91)90412-q.

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11

Valiquette, Claude A. M., Alain D. Lesage, Mireille Cyr, and Jean Toupin. "Computing Cohen’s kappa coefficients using SPSS MATRIX." Behavior Research Methods, Instruments, & Computers 26, no. 1 (March 1994): 60–61. http://dx.doi.org/10.3758/bf03204566.

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12

Kukielka, Andrzej. "Invariant Properties Of Similar Hybrid Matrix Coefficients." IFAC Proceedings Volumes 39, no. 21 (February 2006): 264–68. http://dx.doi.org/10.1016/s1474-6670(17)30195-7.

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13

Douglass, J. Matthew, and Brad Shelton. "On matrix coefficients of the reflection representation." Proceedings of the American Mathematical Society 105, no. 1 (January 1, 1989): 62. http://dx.doi.org/10.1090/s0002-9939-1989-0930242-3.

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14

Wambui Mutoru, J., and Abbas Firoozabadi. "Form of multicomponent Fickian diffusion coefficients matrix." Journal of Chemical Thermodynamics 43, no. 8 (August 2011): 1192–203. http://dx.doi.org/10.1016/j.jct.2011.03.003.

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15

Brubaker, Ben, Daniel Bump, and Solomon Friedberg. "Matrix coefficients and Iwahori–Hecke algebra modules." Advances in Mathematics 299 (August 2016): 247–71. http://dx.doi.org/10.1016/j.aim.2016.05.012.

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16

Le Bris, Claude, Frédéric Legoll, and Simon Lemaire. "On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators." ESAIM: Control, Optimisation and Calculus of Variations 24, no. 4 (October 2018): 1345–80. http://dx.doi.org/10.1051/cocv/2017061.

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We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the equation can be incomplete. A theoretical foundation of the approach in the limit of infinitely small oscillations of the coefficients is provided, using the classical theory of homogenization. We present a comprehensive study of the implementation aspects of our method, and a set of numerical tests and comparisons that show the potential practical interest of the approach. The approach detailed in this article improves on an earlier version briefly presented in [C. Le Bris, F. Legoll and K. Li, C.R. Acad. Sci. Paris, Série I 351 (2013) 265–270].

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17

Naulin, Raúl. "Dichotomies for systems with discontinuous coefficients." Bulletin of the Australian Mathematical Society 45, no. 1 (February 1992): 135–41. http://dx.doi.org/10.1017/s0004972700037072.

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In this work we are concerned with the problem of the existence of an exponential dichotomy for the linear singularly perturbed system εx′ = A(t)x, where the matrix A(t) is piecewise uniformly continuous, that is, A(t) admits points of discontinuity but is uniformly continuous in any interval where it is continuous. We shall prove that the classical result regarding the existence of an exponential dichotomy extends to this case, when there is a constant γ > 0 such that |Reλ(t)| ≥ γ > 0 for any eigenvalue λ(t) of A(t). The proofs are obtained by means of the quasidiagonalisation of a non-constant matrix: For A(t), a piecewise uniformly continuous matrix and σ > 0 there exists a bounded, piecewise constant function L(t): J → ℂn×n, and a bounded matrix Δ(t, σ) such that L-1(t)A(t)L(t) = Λ(t) + Δ(t, σ), |Δ(t, σ)| ≤ σ, where Λ(t) is the diagonal matrix consisting of eigenvalues of A(t).

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18

Brezinski, Claude, and Michela Redivo-Zaglia. "Matrix Shanks Transformations." Electronic Journal of Linear Algebra 35 (February 1, 2019): 248–65. http://dx.doi.org/10.13001/1081-3810.3925.

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Shanks' transformation is a well know sequence transformation for accelerating the convergence of scalar sequences. It has been extended to the case of sequences of vectors and sequences of square matrices satisfying a linear difference equation with scalar coefficients. In this paper, a more general extension to the matrix case where the matrices can be rectangular and satisfy a difference equation with matrix coefficients is proposed and studied. In the particular case of square matrices, the new transformation can be recursively implemented by the matrix $\varepsilon$-algorithm of Wynn. Then, the transformation is related to matrix Pad\'{e}-type and Pad\'{e} approximants. Numerical experiments showing the interest of this transformation end the paper.

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19

Nel, D. G. "A matrix derivation of the asymptotic covariance matrix of sample correlation coefficients." Linear Algebra and its Applications 67 (June 1985): 137–45. http://dx.doi.org/10.1016/0024-3795(85)90191-0.

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20

Muro, Masakazu. "Singular invariant hyperfunctions on the square matrix space and the alternating matrix space." Nagoya Mathematical Journal 169 (2003): 19–75. http://dx.doi.org/10.1017/s0027763000008448.

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AbstractFundamental calculations on singular invariant hyperfunctions on the n ×n square matrix space and on the 2n × 2n alternating matrix space are considered in this paper. By expanding the complex powers of the determinant function or the Pfaffian function into the Laurent series with respect to the complex parameter, we can construct singular invariant hyperfunctions as their Laurent expansion coefficients. The author presents here the exact orders of the poles of the complex powers and determines the exact supports of the Laurent expansion coefficients. By applying these results, we prove that every quasi-relatively invariant hyperfunction can be expressed as a linear combination of the Laurent expansion coefficients of the complex powers and that every singular quasi-relatively invariant hyperfunction is in fact relatively invariant on the generic points of its support. In the last section, we give the formula of the Fourier transforms of singular invariant tempered distributions.

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21

Tadic, Goran, Branko Pejovic, Miladin Gligoric, and Vladan Micic. "Determination of stoichiometric coefficients by the matrix method." Chemical Industry 61, no. 1 (2007): 18–22. http://dx.doi.org/10.2298/hemind0701018t.

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The problem of calculating stoichiometric coefficients in a chemical equation can be solved by standard methods and the method of multidimensional vector space, but good knowledge of vector algebra is required. In this paper, the authors proposed a matrix method and other treatment of the problem was given as the authors' own interpretation. A matrix was formed in the form of base using all the elements which take place in a chemical reaction, after which the matrixes of all the chemical compounds were determined based on numerical indexes and element symbols. This approach enables the setting of a principal matrix equation based on a mathematical approach. The solutions of this matrix equation are the desired stoichiometric coefficients that form a balanced equation. A new approach to tabular solving is presented. This method, compared to existing standard methods, is faster, simpler, and more effective, especially for complex chemical equations. The method was tasted on examples from inorganic chemistry and metallurgy.

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22

Lehner, Franz. "Computing norms of free operators with matrix coefficients." American Journal of Mathematics 121, no. 3 (1999): 453–86. http://dx.doi.org/10.1353/ajm.1999.0022.

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23

Bolhasani, Mostafa, Esmaeil Kavousi Ghafi, Seyed Ali Ghorashi, and Esfandiar Mehrshahi. "Waveform covariance matrix design using Fourier series coefficients." IET Signal Processing 13, no. 5 (July 2019): 562–67. http://dx.doi.org/10.1049/iet-spr.2019.0024.

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24

Avramidi),),), I. G., and R. Schimming). "Heat kernel coefficients for the matrix Schrödinger operator." Journal of Mathematical Physics 36, no. 9 (September 1995): 5042–54. http://dx.doi.org/10.1063/1.531213.

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25

Spronk, Nico, and Ross Stokke. "Matrix coefficients of unitary representations and associated compactifications." Indiana University Mathematics Journal 62, no. 1 (2013): 99–148. http://dx.doi.org/10.1512/iumj.2013.62.4825.

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26

Corwin, Lawrence, and Calvin C. Moore. "$L^p$ Matrix Coefficients for Nilpotent Lie Groups." Rocky Mountain Journal of Mathematics 26, no. 2 (June 1996): 523–44. http://dx.doi.org/10.1216/rmjm/1181072072.

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27

Cameron, Thomas. "Spectral Bounds for Matrix Polynomials with Unitary Coefficients." Electronic Journal of Linear Algebra 30 (February 8, 2015): 585–91. http://dx.doi.org/10.13001/1081-3810.2911.

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It is well known that the eigenvalues of any unitary matrix lie on the unit circle. The purpose of this paper is to prove that the eigenvalues of any matrix polynomial, with unitary coefficients, lie inside the annulus A_{1/2,2) := {z â C | 1/2 < |z| < 2}. The foundations of this result rely on an operator version of Roucheâs theorem and the intermediate value theorem.

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28

Clarke, B. R. "Structure of matrix perturbation coefficients for anharmonic oscillators." Journal of Physics A: Mathematical and General 18, no. 14 (October 1, 1985): 2729–36. http://dx.doi.org/10.1088/0305-4470/18/14/023.

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29

R, Clarke B. "Structure of matrix perturbation coefficients for anharmonic oscillators." Journal of Physics A: Mathematical and General 19, no. 17 (December 1986): 3711. http://dx.doi.org/10.1088/0305-4470/19/17/536.

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30

Konstantinov, O. O. "Two-Term Differential Equations with Matrix Distributional Coefficients." Ukrainian Mathematical Journal 67, no. 5 (October 2015): 711–22. http://dx.doi.org/10.1007/s11253-015-1109-x.

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31

Veliev, O. A. "On the Differential Operators with Periodic Matrix Coefficients." Abstract and Applied Analysis 2009 (2009): 1–21. http://dx.doi.org/10.1155/2009/934905.

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We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then by using these asymptotic formulas, we find conditions on the coefficients for which the number of gaps in the spectrum of the self-adjoint differential operator with the periodic matrix coefficients is finite.

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32

El-Azhar, H. "The matrix Toda equations for coefficients of a matrix three-term recurrence relation." Operators and Matrices, no. 4 (2019): 1125–45. http://dx.doi.org/10.7153/oam-2019-13-75.

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33

Dill, Dan. "Implementing matrix mechanics in Mathematica: Determination of Clebsch–Gordan coefficients by matrix diagonalization." Computers in Physics 5, no. 6 (1991): 616. http://dx.doi.org/10.1063/1.168419.

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34

CERCHIAI, BIANCA L., and BRUNO ZUMINO. "SOME REMARKS ON UNILATERAL MATRIX EQUATIONS." Modern Physics Letters A 16, no. 04n06 (February 28, 2001): 191–96. http://dx.doi.org/10.1142/s0217732301003267.

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We briefly review the results of our paper4: We study certain perturbative solutions of left-unilateral matrix equations. These are algebraic equations where the coefficients and the unknown are square matrices of the same order, or, more abstractly, elements of an associative, but possibly noncommutative algebra, and all coefficients are on the left. Recently such equations have appeared in a discussion of generalized Born–Infeld theories. In particular, two equations, their perturbative solutions and the relation between them are studied, applying a unified approach based on the generalized Bezout theorem for matrix polynomials.

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35

Kostrub, Irina Dmitrievna. "HURWITZ MATRIX, LYAPUNOV AND DIRICHLET ON THE SUSTAINABILITY OF LYAPUNOV’S." Tambov University Reports. Series: Natural and Technical Sciences, no. 123 (2018): 431–36. http://dx.doi.org/10.20310/1810-0198-2018-23-123-431-436.

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The concepts of Hurwitz, Lyapunov and Dirichlet matrices are introduced for the convenience of the stability of linear systems with constant coefficients. They allow us to describe all the cases of interest in the stability theory of linear systems with constant coefficients. A similar classification is proposed for systems of linear differential equations with periodic coefficients. Monodromy matrices of such systems can be either Hurwitz matrices or Lyapunov matrices or Dirichlet matrices (in the discrete sense) in a stable case. The new material relates to systems with variable coefficients.

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36

Ikramov, Kh D., and Yu O. Vorontsov. "Numerical solution of Sylvester matrix equations with normal coefficients." Moscow University Computational Mathematics and Cybernetics 41, no. 4 (October 2017): 153–56. http://dx.doi.org/10.3103/s0278641917040045.

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37

Sha Junchen, Xing Jianping, Gao Liang, and Liang Haozhe. "New Matrix-weight IMM Algorithm Based on Coefficients Filters." INTERNATIONAL JOURNAL ON Advances in Information Sciences and Service Sciences 4, no. 15 (August 31, 2012): 111–18. http://dx.doi.org/10.4156/aiss.vol4.issue15.14.

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38

Curtain, Ruth, and Leiba Rodman. "Analytic Solutions of Matrix Riccati Equations with Analytic Coefficients." SIAM Journal on Matrix Analysis and Applications 31, no. 4 (January 2010): 2075–92. http://dx.doi.org/10.1137/090775002.

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39

Gaigalas, Gediminas, and Stephan Fritzsche. "Calculation of reduced coefficients and matrix elements in -coupling." Computer Physics Communications 134, no. 1 (February 2001): 86–96. http://dx.doi.org/10.1016/s0010-4655(00)00176-4.

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40

LeSage, James, and Yao-Yu Chih. "A Matrix Exponential Spatial Panel Model with Heterogeneous Coefficients." Geographical Analysis 50, no. 4 (December 21, 2017): 422–53. http://dx.doi.org/10.1111/gean.12152.

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41

Gould, M. D., J. Links, and A. J. Bracken. "Matrix elements and Wigner coefficients for Uq[gl(n)]." Journal of Mathematical Physics 33, no. 3 (March 1992): 1008–22. http://dx.doi.org/10.1063/1.529986.

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42

Zhanatauov, Sapargali Utepovich. "A MATRIX OF VALUES THE COEFFICIENTS OF COMBINATIONAL PROPORTIONALITY." Theoretical & Applied Science 71, no. 03 (March 30, 2019): 401–19. http://dx.doi.org/10.15863/tas.2019.03.71.31.

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43

Holík, Miroslav, and Josef Halámek. "Transformation of a Free-Wilson Matrix into Fourier Coefficients." Quantitative Structure-Activity Relationships 20, no. 5-6 (December 2001): 422–28. http://dx.doi.org/10.1002/1521-3838(200112)20:5/6<422::aid-qsar422>3.0.co;2-z.

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44

Dooley, A. H., and R. W. Raffoul. "Matrix coefficients and coadjoint orbits of compact Lie groups." Proceedings of the American Mathematical Society 135, no. 08 (March 22, 2007): 2567–72. http://dx.doi.org/10.1090/s0002-9939-07-08781-3.

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45

Braeutigam, I. N. "Spectral Properties of Matrix Differential Equations with Nonsmooth Coefficients." Differential Equations 56, no. 6 (June 2020): 685–95. http://dx.doi.org/10.1134/s0012266120060026.

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46

Artzrouni, Marc, and Olivier Gavart. "Nonlinear Matrix Iterative Processes and Generalized Coefficients of Ergodicity." SIAM Journal on Matrix Analysis and Applications 21, no. 4 (January 2000): 1343–53. http://dx.doi.org/10.1137/s0895479898348969.

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47

Sanches, I. "From LPC to normalised autocorrelation coefficients through a matrix." Electronics Letters 34, no. 4 (1998): 333. http://dx.doi.org/10.1049/el:19980310.

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48

Gadoev, Makhmadrakhim Gafurovich, and Sulaimon Abunasrovich Iskhokov. "Spectral properties of degenerate elliptic operators with matrix coefficients." Ufimskii Matematicheskii Zhurnal 5, no. 4 (2013): 37–48. http://dx.doi.org/10.13108/2013-5-4-37.

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49

Sun, Binyong. "Bounding matrix coefficients for smooth vectors of tempered representations." Proceedings of the American Mathematical Society 137, no. 01 (August 6, 2008): 353–57. http://dx.doi.org/10.1090/s0002-9939-08-09598-1.

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50

Li, Jian-Shu, and Chen-Bo Zhu. "On the decay of matrix coefficients for exceptional groups." Mathematische Annalen 305, no. 1 (May 1996): 249–70. http://dx.doi.org/10.1007/bf01444220.

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