Study of left rank-preserving complex matrices

Zehui Zhao

doi:10.61383/ejam.20242383

Authors

Zehui Zhao School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou 431000, P.R. China https://orcid.org/0009-0008-0516-7797

DOI:

https://doi.org/10.61383/ejam.20242383

Keywords:

complex matrix, rank of matrices, left (right) rank-preserving matrix, Binet-Cauchy's formula

Abstract

In this paper, we give the notions of left rank-preserving and right rank-preserving matrices and get three equivalent conditions of a left rank-preserving complex matrix. Furthermore, we obtain a kind of classification for the whole $m \times n$ left rank-preserving complex matrices if $m \leq 3$ or $n \leq 3$ .

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