Matrix refinement equations: Continuity and smoothness

Xing-Gang He; Chun-Tai Liu

The Re-nonnegative definite solutions to the matrix equation $A X B = C$

Qing Wen Wang, Chang Lan Yang (1998)

Commentationes Mathematicae Universitatis Carolinae

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An $n \times n$ complex matrix $A$ is called Re-nonnegative definite (Re-nnd) if the real part of $x^{*} A x$ is nonnegative for every complex $n$ -vector $x$ . In this paper criteria for a partitioned matrix to be Re-nnd are given. A necessary and sufficient condition for the existence of and an expression for the Re-nnd solutions of the matrix equation $A X B = C$ are presented.

Reduction of the modified Poincaré differential equation to Birkhoff matrix form

Ice B. Risteski (2001)

Archivum Mathematicum

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In this paper the reduction of the modified Poincaré linear differential equation with one $n$ -tuple regular singularity to the Birkhoff canonical matrix form is given.

Displaying similar documents to “Matrix refinement equations: Continuity and smoothness”

The Re-nonnegative definite solutions to the matrix equation A X B = C

Reduction of the modified Poincaré differential equation to Birkhoff matrix form

The Re-nonnegative definite solutions to the matrix equation $A X B = C$