<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This paper discusses the invariance of the rank of a matrix, the conditions and applications of matrix inequalities, the relationship between matrix rank and matrix operations, the relationship with matrix reversibility, the linear correlation with vector groups and the zero relationship of eigenvalue algebra multiples and other properties. The application of the rank of the matrix in linear algebra, analytic geometry, probability theory, etc. is obtained.</p>
</abstract>

This paper discusses the invariance of the rank of a matrix, the conditions and applications of matrix inequalities, the relationship between matrix rank and matrix operations, the relationship with matrix reversibility, the linear correlation with vector groups and the zero relationship of eigenvalue algebra multiples and other properties. The application of the rank of the matrix in linear algebra, analytic geometry, probability theory, etc. is obtained.

Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations

Shijiazhuang Posts and Telecommunications Technical College

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

This paper discusses the invariance of the rank of a matrix, the conditions and applications of matrix inequalities, the relationship between matrix rank and...

Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations

Published Online: Nov 22, 2021

Page range: 103 - 114

Received: Jun 17, 2021

Accepted: Sep 24, 2021

DOI: https://doi.org/10.2478/amns.2021.2.00139

Keywords
matrix rank, matrix rank invariance, matrix rank inequality, matrix rank identity, linear equations, zero eigenvalue algebraic multiples, homogeneous linear equations

© 2021 Jiying Ma, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations

Published Online: Nov 22, 2021

Page range: 103 - 114

Received: Jun 17, 2021

Accepted: Sep 24, 2021

DOI: https://doi.org/10.2478/amns.2021.2.00139

Keywordsmatrix rank, matrix rank invariance, matrix rank inequality, matrix rank identity, linear equations, zero eigenvalue algebraic multiples, homogeneous linear equations

© 2021 Jiying Ma, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
matrix rank, matrix rank invariance, matrix rank inequality, matrix rank identity, linear equations, zero eigenvalue algebraic multiples, homogeneous linear equations