Inequalities Involving the Inverses of Positive Definite Matrices
نویسندگان
چکیده
منابع مشابه
Determinantal inequalities for positive definite matrices
Let Ai , i = 1, . . . ,m , be positive definite matrices with diagonal blocks A ( j) i , 16 j 6 k , where A ( j) 1 , . . . ,A ( j) m are of the same size for each j . We prove the inequality det( m ∑ i=1 A−1 i ) > det( m ∑ i=1 (A (1) i ) −1) · · ·det( m ∑ i=1 (A (k) i ) −1) and more determinantal inequalities related to positive definite matrices.
متن کاملMatrices with Positive Definite Hermitian Part : Inequalities and Linear
The Hermitian and skew-Hermitian parts of a square matrix A are deened by H(A) (A + A)=2 and S(A) (A ? A)=2: We show that the function f(A) = (H(A ?1)) ?1 is convex with respect to the Loewner partial order on the cone of matrices with positive deenite Hermitian part. That is, for any matrices A and B with positive deenite Hermitian part ff(A) + f(B)g=2 ? f(fA + Bg=2) is positive semideenite: U...
متن کاملSingular value inequalities for positive semidefinite matrices
In this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl. 308 (2000) 203-211] and [Linear Algebra Appl. 428 (2008) 2177-2191].
متن کاملInequalities Involving Khatri-rao Products of Positive Semidefinite Hermitian Matrices
In this paper, we obtain some matrix inequalities in Löwner partial ordering for Khatri-Rao products of positive semidefinite Hermitian matrices. Furthermore, we generalize the Oppenheim’s inequality, with which we will improve some recent results.
متن کاملPersistently positive inverses of perturbed M-matrices
A well known property of anM-matrixA is that the inverse is element-wise non-negative, which we write asA−1 0. In this paper we consider perturbations ofM-matrices and obtain bounds on the perturbations so that the non-negative inverse persists. The bounds are written in terms of decay estimates which characterize the decay (along rows) of the elements of the inverse matrix. We obtain results f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1979
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500027735