Matrix decomposition

Matrix decompositions are mathematical operations that transforms a given matrix to some canonical form.

For example, the singular value decomposition for matrix M is

<math>\mathbf M = U\Sigma V^*</math>

where U is an m-by-m unitary matrix over K, V is an n-by-n unitary matrix over K, and Σ is an m-by-n diagonal matrix whose diagonal entries Σ_i,i are non-negative real numbers.

Most common matrix decompositions are:

• Singular value decomposition
• Cholesky decomposition
• LU decomposition
• Schur decomposition[?]