摘要
给出两个分块矩阵相似的两个充分必要条件 .也就是说 ,如果两个方阵 A和 B在 A2 =0和 B2 =0的条件下 ,则两个分块矩阵 A C0 B 和 A 00 B 相似的充分必要条件是 :rank A C0 B =rank(A) +rank(B)和 AC +CB =0 .如果两个方阵 A和 B在 A2 =A和 B2 =B的条件下 ,则两个分块矩阵 A C0 B和 A 00 B 相似的充分必要条件是 :AC +CB =C.
In this note, we show the two necessary and sufficient conditions such that two block matrices are similar, that is, suppose that the two square matrices A and B satisfy A2=0 and B2=0. Show that the two block matrices AC=0B and A0=0B are similar if and only if rank AC=0B=rank(A)+rank(B) and AC+CB=0. Suppose that the two square matrices A and B satisfy A2=A and B2=B. Show that the two block matrices AC=0B and A0=0B are similar if and only if AC+CB=C.
出处
《数学的实践与认识》
CSCD
北大核心
2005年第3期191-194,共4页
Mathematics in Practice and Theory
关键词
分块矩阵
相似性
充分必要条件
逆
秩
值域
rank of matrix
range of matrix
inverse of matrix
similar matrices
