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Journal articles on the topic 'Positive-definite matrices'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

Töllis, Theodore. "On means of positive definite matrices." Czechoslovak Mathematical Journal 37, no. 4 (1987): 628–41. http://dx.doi.org/10.21136/cmj.1987.102190.

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2

Mostajeran, Cyrus, and Rodolphe Sepulchre. "Ordering positive definite matrices." Information Geometry 1, no. 2 (May 15, 2018): 287–313. http://dx.doi.org/10.1007/s41884-018-0003-7.

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3

Rosen, Lon. "Positive Powers of Positive Positive Definite Matrices." Canadian Journal of Mathematics 48, no. 1 (February 1, 1996): 196–209. http://dx.doi.org/10.4153/cjm-1996-009-9.

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AbstractLet C be an n x n positive definite matrix. If C ≥ 0 in the sense that Cij ≥ 0 and if p > n — 2, then Cp ≥ 0. This implies the following "positive minorant property" for the norms ‖A‖p = [tr(A*A)p/2]1/P. Let 2 < p ≠ 4, 6, … . Then 0 ≤ A ≤ B => ‖A‖p ≥ ‖B‖P if and only if n < p/2 + 1.

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4

Fiedler, Miroslav, and Vlastimil Pták. "A new positive definite geometric mean of two positive definite matrices." Linear Algebra and its Applications 251 (January 1997): 1–20. http://dx.doi.org/10.1016/0024-3795(95)00540-4.

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5

Markham, Thomas L. "Oppenheim's Inequality for Positive Definite Matrices." American Mathematical Monthly 93, no. 8 (October 1986): 642. http://dx.doi.org/10.2307/2322329.

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6

Gilbert, George T. "Positive Definite Matrices and Sylvester's Criterion." American Mathematical Monthly 98, no. 1 (January 1991): 44. http://dx.doi.org/10.2307/2324036.

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7

Cui, Jianlian, Chi-Kwong Li, and Nung-Sing Sze. "Products of positive semi-definite matrices." Linear Algebra and its Applications 528 (September 2017): 17–24. http://dx.doi.org/10.1016/j.laa.2015.09.045.

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8

Ichi Fujii, Jun, and Masatoshi Fujii. "Kolmogorov's complexity for positive definite matrices." Linear Algebra and its Applications 341, no. 1-3 (January 2002): 171–80. http://dx.doi.org/10.1016/s0024-3795(01)00354-8.

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9

Markham, Thomas L. "Oppenheim's Inequality for Positive Definite Matrices." American Mathematical Monthly 93, no. 8 (October 1986): 642–44. http://dx.doi.org/10.1080/00029890.1986.11971910.

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10

Gilbert, George T. "Positive Definite Matrices and Sylvester's Criterion." American Mathematical Monthly 98, no. 1 (January 1991): 44–46. http://dx.doi.org/10.1080/00029890.1991.11995702.

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11

Zaidi, A. "Positive definite combination of symmetric matrices." IEEE Transactions on Signal Processing 53, no. 11 (November 2005): 4412–16. http://dx.doi.org/10.1109/tsp.2005.855077.

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12

Brualdi, Richard A., Suk-Geun Hwang, and Sung-Soo Pyo. "Vector majorization via positive definite matrices." Linear Algebra and its Applications 257 (May 1997): 105–20. http://dx.doi.org/10.1016/s0024-3795(96)00042-0.

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13

朱, 佳政. "Decomposition of Symmetric Positive Definite Matrices." Pure Mathematics 09, no. 04 (2019): 503–13. http://dx.doi.org/10.12677/pm.2019.94067.

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14

ik Choi, Daes. "Determinantal inequalities of positive definite matrices." Mathematical Inequalities & Applications, no. 1 (2016): 167–72. http://dx.doi.org/10.7153/mia-19-12.

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15

Johnson, Charles R., and Wayne W. Barrett. "Determinantal inequalities for positive definite matrices." Discrete Mathematics 119, no. 1-3 (August 1993): 97–106. http://dx.doi.org/10.1016/0012-365x(93)90119-e.

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16

Quintana, Yamilet, and José M. Rodríguez. "Measurable diagonalization of positive definite matrices." Journal of Approximation Theory 185 (September 2014): 91–97. http://dx.doi.org/10.1016/j.jat.2014.06.003.

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17

Itai, Uri, and Nir Sharon. "Subdivision Schemes for Positive Definite Matrices." Foundations of Computational Mathematics 13, no. 3 (July 20, 2012): 347–69. http://dx.doi.org/10.1007/s10208-012-9131-y.

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18

Choudhury, Dipa, Roger A. Horn, and Stephen J. Pierce. "Quasi-positive definite operators and matrices." Linear Algebra and its Applications 99 (February 1988): 161–76. http://dx.doi.org/10.1016/0024-3795(88)90130-9.

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19

Granario, Daryl Q., and Tin-Yau Tam. "Products of positive definite symplectic matrices." Linear Algebra and its Applications 626 (October 2021): 188–203. http://dx.doi.org/10.1016/j.laa.2021.05.016.

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20

Al-homidan, S., and M. Alshahrani. "Positive Definite Hankel Matrices Using Cholesky Factorization." Computational Methods in Applied Mathematics 9, no. 3 (2009): 221–25. http://dx.doi.org/10.2478/cmam-2009-0013.

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AbstractReal positive definite Hankel matrices arise in many important applications. They have spectral condition numbers which exponentially increase with their orders. We give a structural algorithm for finding positive definite Hankel matrices using the Cholesky factorization, compute it for orders less than or equal to 30, and compare our result with earlier results.

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21

Wei Wei, Wei Wei, Qiao Ke Wei Wei, Fan Gao Qiao Ke, Rafał Scherer Fan Gao, and Shujia Fan Rafał Scherer. "Sufficient Conditions Analysis of Coverage Algorithm Constructed Positive Definite Tridiagonal Matrices in WSNs." 網際網路技術學刊 22, no. 4 (July 2021): 735–41. http://dx.doi.org/10.53106/160792642021072204002.

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22

Niezgoda, Marek. "On $f$-connections of positive definite matrices." Annals of Functional Analysis 5, no. 2 (2014): 147–57. http://dx.doi.org/10.15352/afa/1396833510.

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23

Howroyd, Upton, and Wood. "Fractional Hadamard Powers of Positive Definite Matrices." Real Analysis Exchange 15, no. 1 (1989): 21. http://dx.doi.org/10.2307/44151980.

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24

Dutour Sikirić, Mathieu, Anna Haensch, John Voight, and Wessel P. J. van Woerden. "A canonical form for positive definite matrices." Open Book Series 4, no. 1 (December 29, 2020): 179–95. http://dx.doi.org/10.2140/obs.2020.4.179.

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25

Bourin, Jean-Christophe, and Eun-Young Lee. "Direct sums of positive semi-definite matrices." Linear Algebra and its Applications 463 (December 2014): 273–81. http://dx.doi.org/10.1016/j.laa.2014.09.012.

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26

Varah, J. M. "Positive definite Hankel matrices of minimal condition." Linear Algebra and its Applications 368 (July 2003): 303–14. http://dx.doi.org/10.1016/s0024-3795(02)00685-7.

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27

Sivalingam, Ravishankar, Daniel Boley, Vassilios Morellas, and Nikolaos Papanikolopoulos. "Tensor Dictionary Learning for Positive Definite Matrices." IEEE Transactions on Image Processing 24, no. 11 (November 2015): 4592–601. http://dx.doi.org/10.1109/tip.2015.2440766.

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28

Bhatia, Rajendra, and Tanvi Jain. "On symplectic eigenvalues of positive definite matrices." Journal of Mathematical Physics 56, no. 11 (November 2015): 112201. http://dx.doi.org/10.1063/1.4935852.

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29

Cherian, Anoop, Vassilios Morellas, and Nikolaos Papanikolopoulos. "Bayesian Nonparametric Clustering for Positive Definite Matrices." IEEE Transactions on Pattern Analysis and Machine Intelligence 38, no. 5 (May 1, 2016): 862–74. http://dx.doi.org/10.1109/tpami.2015.2456903.

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30

Fiedler, Miroslav. "Old and new about positive definite matrices." Linear Algebra and its Applications 484 (November 2015): 496–503. http://dx.doi.org/10.1016/j.laa.2015.07.016.

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31

Rothman, A. J. "Positive definite estimators of large covariance matrices." Biometrika 99, no. 3 (June 18, 2012): 733–40. http://dx.doi.org/10.1093/biomet/ass025.

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32

Olkin, I., and S. T. Rachev. "Maximum Submatrix Traces for Positive Definite Matrices." SIAM Journal on Matrix Analysis and Applications 14, no. 2 (April 1993): 390–97. http://dx.doi.org/10.1137/0614027.

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33

Lee, Hosoo. "Weighted Carlson Mean of Positive Definite Matrices." Kyungpook mathematical journal 53, no. 3 (September 23, 2013): 479–95. http://dx.doi.org/10.5666/kmj.2013.53.3.479.

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34

Amodio, P., F. Iavernaro, and D. Trigiante. "Conservative perturbations of positive definite Hamiltonian matrices." Numerical Linear Algebra with Applications 12, no. 2-3 (2005): 117–25. http://dx.doi.org/10.1002/nla.409.

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35

Sivalingam, Ravishankar, Daniel Boley, Vassilios Morellas, and Nikolaos Papanikolopoulos. "Tensor Sparse Coding for Positive Definite Matrices." IEEE Transactions on Pattern Analysis and Machine Intelligence 36, no. 3 (March 2014): 592–605. http://dx.doi.org/10.1109/tpami.2013.143.

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36

Sra, Suvrit. "Positive definite matrices and the S-divergence." Proceedings of the American Mathematical Society 144, no. 7 (October 22, 2015): 2787–97. http://dx.doi.org/10.1090/proc/12953.

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37

Lasserre, J. B. "Linear programming with positive semi-definite matrices." Mathematical Problems in Engineering 2, no. 6 (1996): 499–522. http://dx.doi.org/10.1155/s1024123x96000452.

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We consider the general linear programming problem over the cone of positive semi-definite matrices. We first provide a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution. We then simply characterize the analogues of the standard concepts of linear programming, i.e., extreme points, basis, reduced cost, degeneracy, pivoting step as well as a Simplex-like algorithm.

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38

Mathias, Roy. "Spectral Perturbation Bounds for Positive Definite Matrices." SIAM Journal on Matrix Analysis and Applications 18, no. 4 (October 1997): 959–80. http://dx.doi.org/10.1137/s0895479894271081.

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39

Gselmann, Eszter. "Jordan triple mappings on positive definite matrices." Aequationes mathematicae 89, no. 3 (February 8, 2014): 629–39. http://dx.doi.org/10.1007/s00010-013-0251-5.

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40

Cerdeira, J. Orestes, Isabel Faria, and Paulo Bárcia. "Establishing determinantal inequalities for positive-definite matrices." Discrete Applied Mathematics 63, no. 1 (October 1995): 13–24. http://dx.doi.org/10.1016/0166-218x(94)00027-b.

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41

Fischer, P., and J. D. Stegeman. "Functions operating on positive-definite symmetric matrices." Journal of Mathematical Analysis and Applications 171, no. 2 (December 1992): 461–70. http://dx.doi.org/10.1016/0022-247x(92)90358-k.

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42

Kuznetsov, Yu I. "Connection between positive-definite and Hessenberg matrices." Siberian Mathematical Journal 27, no. 2 (1987): 211–16. http://dx.doi.org/10.1007/bf00969388.

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43

Lim, Yongdo. "Invariant tolerance relations on positive definite matrices." Linear Algebra and its Applications 619 (June 2021): 1–11. http://dx.doi.org/10.1016/j.laa.2021.02.008.

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44

Sivakumar, K., Ar Meenakshi, and Projesh Choudhury. "Almost Definite Matrices Revisited." Electronic Journal of Linear Algebra 29 (September 20, 2015): 102–19. http://dx.doi.org/10.13001/1081-3810.2969.

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A real matrix A is called as an almost definite matrix if â¨x, Axâ© = 0 â Ax = 0. This notion is revisited. Many basic properties of such matrices are established. Several characterizations for a matrix to be an almost definite matrix are presented. Comparisons of certain properties of almost definite matrices with similar properties for positive definite or positive semidefinite matrices are brought to the fore. Interconnections with matrix classes arising in the theory of linear complementarity problems are discussed briefly.

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45

Filipiak, Katarzyna, Augustyn Markiewicz, Adam Mieldzioc, and Aneta Sawikowska. "On Projection of a Positive Definite Matrix on a Cone of Nonnegative Definite Toeplitz Matrices." Electronic Journal of Linear Algebra 33 (May 16, 2018): 74–82. http://dx.doi.org/10.13001/1081-3810.3750.

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We consider approximation of a given positive definite matrix by nonnegative definite banded Toeplitz matrices. We show that the projection on linear space of Toeplitz matrices does not always preserve nonnegative definiteness. Therefore we characterize a convex cone of nonnegative definite banded Toeplitz matrices which depends on the matrix dimensions, and we show that the condition of positive definiteness given by Parter [{\em Numer. Math. 4}, 293--295, 1962] characterizes the asymptotic cone. In this paper we give methodology and numerical algorithm of the projection basing on the properties of a cone of nonnegative definite Toeplitz matrices. This problem can be applied in statistics, for example in the estimation of unknown covariance structures under the multi-level multivariate models, where positive definiteness is required. We conduct simulation studies to compare statistical properties of the estimators obtained by projection on the cone with a given matrix dimension and on the asymptotic cone.

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46

Neubauer, M. "An Inequality for Positive Definite Matrices With Applications to Combinatorial Matrices." Linear Algebra and its Applications 267, no. 1-3 (December 1997): 163–74. http://dx.doi.org/10.1016/s0024-3795(97)00006-2.

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47

Neubauer, Michael G. "An inequality for positive definite matrices with applications to combinatorial matrices." Linear Algebra and its Applications 267 (December 1997): 163–74. http://dx.doi.org/10.1016/s0024-3795(97)80048-1.

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48

Chehab, Jean-Paul, and Marcos Raydan. "Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices." Mathematics 4, no. 3 (July 9, 2016): 46. http://dx.doi.org/10.3390/math4030046.

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49

Ikramov, Kh D. "On the Symplectic Eigenvalues of Positive Definite Matrices." Moscow University Computational Mathematics and Cybernetics 42, no. 1 (January 2018): 1–4. http://dx.doi.org/10.3103/s0278641918010041.

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50

Lim, Yongdo. "Factorizations and geometric means of positive definite matrices." Linear Algebra and its Applications 437, no. 9 (November 2012): 2159–72. http://dx.doi.org/10.1016/j.laa.2012.05.039.

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