  Diagonalization, or eigenvalue decomposition, is very useful in many areas of
applied mathematics, including signal processing and quantum physics. Matrix
decomposition is also a useful tool for approximating matrices as the product
of a matrix and its transpose, which relates to unitary diagonalization. As
stated by the spectral theorem, only normal matrices are unitarily
diagonalizable. However we show that all real square matrices are the real part
of some unitarily diagonalizable matrix.
