Matrices That Commute with Their Conjugate and Transpose ()
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.
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.
Conflicts of Interest
The authors declare no conflicts of interest.
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
|