Review Note

Fact 3.2. The spectral theorem says: A square matrix \( \mathbf{A} \) is diagonalizable by a unitary matrix if and only if \( \mathbf{A} \) is a {{c1::normal}} matrix.

For example, diagonalizable in a unitary eigendecomposition, there exists \( \mathbf{V} \) unitary and \( \mathbf{\Lambda} \) diagonal such that \( \mathbf{A} = \mathbf{V} \mathbf{\Lambda} \mathbf{V}' \),

pg. 3.9