Editing Spectral theorem (section)

=== Spectral decomposition and the singular value decomposition ===

The spectral decomposition is a special case of the [[singular value decomposition]], which states that any matrix  <math>A \in \mathbb{C}^{m \times n}</math> can be expressed as 
<math>A = U\Sigma V^{*}</math>, where <math>U \in \mathbb{C}^{m \times m}</math> and <math>V \in \mathbb{C}^{n \times n}</math> are [[unitary matrices]] and <math>\Sigma \in \mathbb{R}^{m \times n}</math> is a diagonal matrix. The diagonal entries of <math>\Sigma</math> are uniquely determined by <math>A</math> and are known as the [[singular values]] of <math>A</math>. If <math>A</math> is Hermitian, then <math>A^* = A</math> and <math>V \Sigma U^* = U \Sigma V^*</math> which implies <math>U = V</math>.