Matrices That Commute with Their Conjugate and Transpose

• 作者: Geoffrey Goodson
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: Normal MATRIX MATRIX COMMUTING with Its CONJUGATE and TRANSPOSE
• 年，卷（期）: 2013,（3）
• 页码范围: 22-25
• 页数: 4页
• 分类号: O1

摘要

It is known that if A∈Mn is normal (AA*=A*A) , then AA￣=A￣A if and only if AAT=ATA. This leads to the question: do both AA￣=A￣A and AAT=ATA?imply that A?is normal? We give an example to show that this is false when n=4, but we show that it is true when n=2?and n=3.