Simultaneous Diagonalization via Congruence of Hermitian Matrices: Some Equivalent Conditions and a Numerical Solution

Congruence of Hermitian Matrices by Hermitian Matrices

Two Hermitian matrices A, B ∈ Mn(C) are said to be Hermitian-congruent if there exists a nonsingular Hermitian matrix C ∈ Mn(C) such that B = CAC. In this paper, we give necessary and sufficient conditions for two nonsingular simultaneously unitarily diagonalizable Hermitian matrices A and B to be Hermitian-congruent. Moreover, when A and B are Hermitian-congruent, we describe the possible iner...

Joint Approximate Diagonalization of Positive Deenite Hermitian Matrices

This paper provides an iterative algorithm to jointly approximately di-agonalize K Hermitian positive deenite matrices ? 1 , : : : , ? K. Speciically it calculates the matrix B which minimizes the criterion P K k=1 n k log det diag(BC k B) ? log det(BC k B)], n k being positive numbers, which is a measure of the deviation from diagonality of the matrices BC k B. The convergence of the algorithm...

Joint Approximate Diagonalization of Positive Definite Hermitian Matrices

Numerical Solution of Optimal Control of Time-varying Singular Systems via Operational Matrices

In this paper, a numerical method for solving the constrained optimal control of time-varying singular systems with quadratic performance index is presented. Presented method is based on Bernste in polynomials. Operational matrices of integration, differentiation and product are introduced and utilized to reduce the optimal control of time-varying singular problems to the solution of algebraic ...

Ela Hermitian Octonion Matrices and Numerical Ranges

Notions of numerical ranges and joint numerical ranges of octonion matrices are introduced. Various properties of hermitian octonion matrices related to eigenvalues and convex cones, such as the convex cone of positive semidefinite matrices, are described. As an application, convexity of joint numerical ranges of 2×2 hermitian matrices is characterized. Another application involves existence of...