一类矩阵秩的性质推广

Generalization of the Properties of the Rank of a Class of Matrices

摘要: 在A^K=0，A^K=A，A^K=E(K≥3)的条件下，证明了A+K_iE(i=1,2,...t)这类矩阵秩的恒等式成立的条件，并给出该等式的具体表达式，改进了当A²=0，A²=A时，一类矩阵秩的恒等式成立的条件。

Abstract: Under the condition of A^K=0，A^K=A，A^K=E(K≥3), this paper proved the conditions for the establishment of identical relation about the rank of a class of matrices that A+K_iE(i=1,2,...t), gave the specific expression of the equality, when A²=0, A²=A, and improved the conditions for the establishment of identical relation about the rank of a class of matrices.