The minimal rank of A-BX with respect to Hermitian matrix

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摘要

In this paper, we discuss the minimal rank of A-BX when X is Hermitian by applying singular value decomposition and some rank equalities of matrices, and obtain a representation of the minimal rank. Based on the representation, we obtain necessary and sufficient conditions for the matrix equation BX=A to have Hermitian solutions.

论文关键词：Singular value decomposition,Hermitian matrix,Rank,Inertia

论文评审过程：Available online 20 February 2014.

论文官网地址：https://doi.org/10.1016/j.amc.2014.01.116