Matrices That Commute with Their Conjugate and Transpose
Geoffrey Goodson
Towson University, Towson, USA.
DOI: 10.4236/alamt.2013.33005   PDF    HTML     6,330 Downloads   13,249 Views   Citations


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.

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Goodson, G. (2013) Matrices That Commute with Their Conjugate and Transpose. Advances in Linear Algebra & Matrix Theory, 3, 22-25. doi: 10.4236/alamt.2013.33005.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Kh. Ikramov, “On the Matrix Equation ,” Moscow University Computational Mathematics and Cybernetics. Vol. 34, No. 2, 2010, pp. 51-55. doi:10.3103/S0278641910020019
[2] G. R. Goodson and R. A. Horn, “Canonical Forms for Normal Matrices That Commute with Their Complex Conjugate,” Linear Algebra and Its Applications, Vol. 430, No. 4, 2009, pp. 1025-1038. doi:10.1016/j.laa.2008.09.039
[3] R. A. Horn and C. R. Johnson, “Matrix Analysis,” Cambridge University Press, New York, 1985. doi:10.1017/CBO9780511810817

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