Matrix decomposition

Matrix decompositions are factorizations of matrices that express them in some canonical form.

For example, the singular value decomposition for matrix M is

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:

• Cholesky decomposition
• Jordan decomposition
• LU decomposition
• Schur decomposition
• Singular value decomposition
• Spectral decomposition
• QR decomposition