Matrices That Commute with Their Conjugate and Transpose

Geoffrey Goodson

Towson University, Towson, USA.

DOI: 10.4236/alamt.2013.33005                

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^TA. This leads to the question: do both AA￣=A￣A and AA^T=A^TA 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.

Keywords

Normal Matrix; Matrix Commuting with Its Conjugate and Transpose

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[3]	R. A. Horn and C. R. Johnson, “Matrix Analysis,” Cambridge University Press, New York, 1985. doi:10.1017/CBO9780511810817