关于分块矩阵相似性的探讨
On the Similarity of Block Matrix
DOI: 10.12677/AAM.2021.104120, PDF,    科研立项经费支持
作者: 程 宇：保定学院数据科学与软件工程学院，河北 保定
关键词: 矩阵的相似；对合矩阵；幂零矩阵；Roth定理；Matrix’s Similarity； Involutory Matrix； Nilpotent Matrix； Roth’s Theory
摘要: 本文在已有文献的基础上，给出了当A1、B1为对合矩阵时，分块矩阵与相似的充分必要条件是A1C+CB1=0。当A1、B1为k-幂零矩阵时，上述两分块矩阵相似的充分条件是和A1C+CB1=0。最后对A1、B1为k-幂零矩阵进行了进一步讨论。
Abstract: This article, on the basis of the existing literature, applying Roth’s theory, proves that when the A1 and B1 are involutory matrix, the necessary and sufficient condition of similar partitioned of matrix and is A1C+CB1=0. When A1 and B1 are k-nilpotent matrix, the sufficient condition for the similarity of the two-block matrices is and A1C+CB1=0. At last, we further discuss that A1 and B1 are k-nilpotent matrix.
文章引用：程宇. 关于分块矩阵相似性的探讨[J]. 应用数学进展, 2021, 10(4): 1109-1114. https://doi.org/10.12677/AAM.2021.104120

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