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: