Baojun Yang.  Analysis of the Properties of Matrix Rank and the Relationship between Matrix Rank and Matrix Operations.  Dynamic Systems and Applications 29 (2020) No. 3, 871-880

https://doi.org/10.46719/dsa202029338

ABSTRACT.
This paper discusses the invariance, the conditions inequalities, the relationship between matrix rank and matrix operations, the relationship with matrix reversibility, the linear correlation with vector groups, and zero The 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.

Keywords: matrix rank; matrix rank invariance; matrix rank inequality; matrix rank identity; linear equations; zero eigenvalue algebraic multiples; homogeneous linear equations.