Symmetric Quasidefinite Matrices

On the Stability of Cholesky Factorization for Symmetric Quasidefinite Systems

Sparse linear equations Kd r are considered, where K is a specially structured symmetric indefinite matrix that arises in numerical optimization and elsewhere. Under certain conditions, K is quasidefinite. The Cholesky factorization PKP T LDL T is then known to exist for any permutation P, even though D is indefinite. Quasidefinite matrices have been used successfully by Vanderbei within barrie...

Definite and Quasidefinite Sets of Stochastic Matrices'

Properties of Central Symmetric X-Form Matrices

In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.

Generalized matrix functions, determinant and permanent

In this paper, using permutation matrices or symmetric matrices, necessary and sufficient conditions are given for a generalized matrix function to be the determinant or the permanent. We prove that a generalized matrix function is the determinant or the permanent if and only if it preserves the product of symmetric permutation matrices. Also we show that a generalized matrix function is the de...

The exponential functions of central-symmetric $X$-form matrices

It is well known that the matrix exponential function has practical applications in engineering and applied sciences. In this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric $X$-form. For instance, $e^{mathbf{A}t}$, $t^{mathbf{A}}$ and $a^{mathbf{A}t}$ will be evaluated by the new formulas in this par...