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Normal matrices

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Show that each matrix type is normal.

1. Hermitian
2. skew-Hermitian
3. unitary
4. symmetric
5. skew-symmetric
6. orthogonal

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Solution Summary

This shows how to prove that each matrix type is normal.

Solution Preview

I will use the notation:
A^T = transpose(A)
A^* = complex_conjugate(A)
A^t = (A^T)^* = hermitian_conjugate(A)
A^i = inverse(A)
A matrix, A, is defined to normal if and only if
[A , A^t] = A A^t - A^t A = 0
(comment: A matrix, A, is also normal if and only if there exists a unitary matrix, U, such that (U A U^t) is ...

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