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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 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 ...

    Solution Summary

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