Main Page
|
See live article
|
Alphabetical index
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