# Normal matrices

Show that each matrix type is normal.

1. Hermitian

2. skew-Hermitian

3. unitary

4. symmetric

5. skew-symmetric

6. orthogonal

https://brainmass.com/math/matrices/normal-matrices-2652

#### 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.

$2.19