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
mby
m unitary matrix over
K,
V is an
nby
n unitary matrix over
K, and Σ is an
mby
n diagonal matrix whose diagonal entries Σ
_{i,i} are nonnegative real numbers.
Most common matrix decompositions are: