Matrices That Commute with Their Conjugate and Transpose - Advances in Linear Algebra & Matrix Theory

ALAMT > Vol.3 No.3, September 2013

Matrices That Commute with Their Conjugate and Transpose ()

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DOI: 10.4236/alamt.2013.33005 6,222 Downloads 13,451 Views Citations

Author(s)

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

Share and Cite:

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.

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