矩阵的秩正规形式的一些结果

Pub Date : 2019-12-01 DOI:10.2478/ausm-2019-0028

Sorin Radulescu, Marius Drăgan, M. Bencze

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引用次数: 0

摘要

摘要如果A是秩为r的矩形矩阵，则A可以写成PSQ，其中P和Q是可逆矩阵，s=(IrOOO) s= \左({\矩阵{\ hfill {{\rm{I}}_{\rm{r}}}} & \hfill {\rm{O}} \cr \hfill {\rm{O}} & \hfill {\rm{O}} \cr}} \hfill {\rm{O}} \cr}} \右)。这是矩阵a的秩范式。本文的目的是展示这种表示形式的一些结果。

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Some consequences of the rank normal form of a matrix

Abstract If A is a rectangular matrix of rank r, then A may be written as PSQ where P and Q are invertible matrices and s=(IrOOO) s = \left( {\matrix{ \hfill {{{\rm{I}}_{\rm{r}}}} & \hfill {\rm{O}} \cr \hfill {\rm{O}} & \hfill {\rm{O}} \cr } } \right) . This is the rank normal form of the matrix A. The purpose of this paper is to exhibit some consequences of this representation form.

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