On matrix variance inequalities

On some matrix inequalities

The arithmetic-geometric mean inequality for singular values due to Bhatia and Kittaneh says that 2sj(AB ∗) ≤ sj(A∗A + B∗B), j = 1, 2, . . . for any matrices A,B. We first give new proofs of this inequality and its equivalent form. Then we use it to prove the following trace inequality: Let A0 be a positive definite matrix and A1, . . . , Ak be positive semidefinite matrices. Then tr k ∑

On Some Matrix Trace Inequalities

A is further called positive definite, symbolized A > 0, if the strict inequality in 1.1 holds for all nonzero x ∈ C. An equivalent condition forA ∈ Mn to be positive definite is thatA is Hermitian and all eigenvalues of A are positive real numbers. Given a positive semidefinite matrix A and p > 0, A denotes the unique positive semidefinite pth power of A. Let A and B be two Hermitian matrices ...

On Several Matrix Kantorovich-Type Inequalities

Matrix Trace Inequalities on the Tsallis Entropies

Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis. In addition, some matrix trace inequalities related to the Tsallis relative entropy are studied.

Solubility of Matrix Inequalities

An important part is played in the theory of control by special matrix equations [i], and also by the matrix inequalities associated with them. The solutions of these equations or inequalities allow us to construct Lyapunov functions for nonlinear systems of automatic regulation, and to solve problems of the synthesis of optimal control with quadratic quality criterion. Convenient and effective...