Note on traces of matrix products involving inverses of positive definite ones

• Autorzy: Grzybowski A. Z.

Identyfikatory

DOI

10.17512/jamcm.2018.1.03

• Języki publikacji: EN

Abstrakty

EN

This short note is devoted to the analysis of the trace of a product of two matrices in the case where one of them is the inverse of a given positive definite matrix while the other is nonnegative definite. In particular, a relation between the trace of A^-1 H and the values of diagonal elements of the original matrix A is analysed.

Słowa kluczowe

EN

matrix product; trace inequalities; inverse matrix

PL

ślad macierzy; iloczyn macierzy; macierz odwrotna

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2018
• Tom: Vol. 17, nr 1
• Strony: 29--36
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Grzybowski A. Z.

• Institute of Mathematics, Czestochowa University of Technology Czestochowa, Poland

Bibliografia

• [1] Bao, Y., & Ullah, A. (2010). Expectation of quadratic forms in normal and nonnormal variables with applications. Journal of Statistical Planning and Inference, 140(5), 1193-1205.
• [2] Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. New York: Springer-Verlag.
• [3] Grzybowski, A. (2002). Metody wykorzystania informacji a priori w estymacji parametrów regresji. Seria Monografie No 89. Częstochowa: Wydawnictwo Politechniki Częstochowskiej, 153 (in Polish).
• [4] Ginovyan, M.S., & Sahakyan, A.A. (2013). On the trace approximations of products of Toeplitz matrices. Statistics and Probability Letters, 83, 753-760.
• [5] Magnus, J.R. (1979). The expectation of products of quadratic forms in normal variables: the practice. Statistica Neerlandica, 33, 131-136.
• [6] Chang, D.-W. (1999). A matrix trace inequality for products of Hermitian matrices. Journal of Mathematical Analysis and Applications, 237, 721-725.
• [7] Fang, Y., Loparo, K.A., & Feng, X. (1994). Inequalities for the trace of matrix product. IEEE Transactions On Automatic Control, 39, 12.
• [8] Furuichi, S., Kuriyama, K., & Yanagi, K. (2009). Trace inequalities for products of matrices. Linear Algebra and its Applications, 430, 2271-2276.
• [9] Komaroff, N. (2008). Enhancements to the von Neumann trace inequality. Linear Algebra and its Applications, 428, 738-741.
• [10] Patel, R., & Toda, M. (1979). Trace Inequalities Involving Hermitian Matrices. Linear Algebra and its Applications, 23, 13-20.
• [11] Wang, B.-Y., Xi, B.-Y., & Zhang, F. (1999). Some inequalities for sum and product of positive semidefinite matrices. Linear Algebra and its Applications, 293, 39-49.
• [12] Rao, C.R. (1973). Linear Statistical Inference and Its Applications. New York: John Wiley & Sons.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).