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 wh...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.展开更多
文摘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.
