Matrix Decomposition
In the
mathematical
discipline of
linear algebra
, a
matrix decomposition
is a
factorization
of a
matrix
into some canonical form. There are several different decompositions of a given matrix and the decomposition used depends on the problem we want to solve. In
numerical analysis
for example different decompositions are used to implement efficient matrix
algorithms
.
Example
When solving a
system of linear equations
the matrix
A
can be decomposed via the
LU decomposition
. The LU decomposition factorizes a matrix into a
lower triangular matrix
L
and an
upper triangular matrix
U
. The matrices
L
and
U
are much easier to solve than the original matrix
A
.
See also
Block LU decomposition
Cholesky decomposition
Jordan decomposition
LU decomposition
QR decomposition
Schur decomposition
Singular value decomposition
Spectral decomposition
(also called the
eigendecomposition
)
Proper Orthogonal Decomposition
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