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Matrices That Commute with Their Conjugate and Transpose
Towson University, Towson, USA
- 1 Towson University, Towson, USA
Advances in Linear Algebra & Matrix Theory·Volume 03 (2013)·Pages 22–25·Published 17 September 2013·DOI10.4236/alamt.2013.33005
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Abstract
It is known that if A∈M n is normal (AA * =A * A ) , then AA￣=A￣A if and only if AA T =A T A. This leads to the question: do both AA￣=A￣A and AA T =A T A 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 whe n n=2 and n=3.
KeywordsNormal MatrixMatrix Commuting with Its Conjugate and Transpose
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