If H(A) = (A + A∗)/2 and c is real, it is determined when cH(A-1 − H(A)-1 is positive definite when A is a matrix for which H(A) is positive definite. Motivation is given by considering the classical adjoint, and the result is applied to A-1A∗ and A2.
%0 Journal Article
%1 johnson1973inequality
%A Johnson, Charles R
%D 1973
%J Linear Algebra and its Applications
%K covariance_matrix linear_algebra symmetrization_map
%P 13 - 18
%R http://dx.doi.org/10.1016/0024-3795(73)90003-7
%T An inequality for matrices whose symmetric part is positive definite
%U http://www.sciencedirect.com/science/article/pii/0024379573900037
%V 6
%X If H(A) = (A + A∗)/2 and c is real, it is determined when cH(A-1 − H(A)-1 is positive definite when A is a matrix for which H(A) is positive definite. Motivation is given by considering the classical adjoint, and the result is applied to A-1A∗ and A2.
@article{johnson1973inequality,
abstract = {If H(A) = (A + A∗)/2 and c is real, it is determined when cH(A-1 − H(A)-1 is positive definite when A is a matrix for which H(A) is positive definite. Motivation is given by considering the classical adjoint, and the result is applied to A-1A∗ and A2.},
added-at = {2016-04-10T02:33:40.000+0200},
author = {Johnson, Charles R},
biburl = {https://www.bibsonomy.org/bibtex/27498f33ba29392a7f7f6762eac4536ae/peter.ralph},
doi = {http://dx.doi.org/10.1016/0024-3795(73)90003-7},
interhash = {fcce93d3d8f0742954526db4dd6836cc},
intrahash = {7498f33ba29392a7f7f6762eac4536ae},
issn = {0024-3795},
journal = {Linear Algebra and its Applications},
keywords = {covariance_matrix linear_algebra symmetrization_map},
pages = {13 - 18},
timestamp = {2016-04-10T02:33:40.000+0200},
title = {An inequality for matrices whose symmetric part is positive definite},
url = {http://www.sciencedirect.com/science/article/pii/0024379573900037},
volume = 6,
year = 1973
}