ALAMT  Vol.3 No.3 , September 2013
Matrices That Commute with Their Conjugate and Transpose
Author(s) Geoffrey Goodson*
ABSTRACT

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.


Cite this paper
G. Goodson, "Matrices That Commute with Their Conjugate and Transpose," Advances in Linear Algebra & Matrix Theory, Vol. 3 No. 3, 2013, pp. 22-25. doi: 10.4236/alamt.2013.33005.
References
[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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