For complex matrices, the symmetry AT = A that produces real eigenvalues changes to AT =
Chapter 6, Problem 28(choose chapter or problem)
For complex matrices, the symmetry AT = A that produces real eigenvalues changes to AT = A. From det(A - AI) = 0, find the eigenvalues of the 2 by 2 "Hermitian" matrix A = [4 2 + i; 2 - i 0] = AT. To see why eigenvalues are real when AT = A, adjust equation (1) ofthe text to A x = A x. Transpose to xT AT = xT A. With AT = A, reach equation (2): A = A.
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