Matrices That Commute with Their Conjugate and Transpose

Geoffrey Goodson

doi:10.4236/alamt.2013.33005

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Matrices That Commute with Their Conjugate and Transpose

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DOI: 10.4236/alamt.2013.33005 4,433 Downloads 10,803 Views Citations

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Geoffrey Goodson

Affiliation(s)

Towson University, Towson, USA.

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.

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

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