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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
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