In numerical analysis, different decompositions are used to implement efficient matrix algorithms.
require fewer additions and multiplications to solve, compared with the original system
, though one might require significantly more digits in inexact arithmetic such as floating point.
The Jordan normal form and the Jordan–Chevalley decomposition Refers to variants of existing matrix decompositions, such as the SVD, that are invariant with respect to diagonal scaling.
[3][4] There exist analogues of the SVD, QR, LU and Cholesky factorizations for quasimatrices and cmatrices or continuous matrices.
These factorizations are based on early work by Fredholm (1903), Hilbert (1904) and Schmidt (1907).
For an account, and a translation to English of the seminal papers, see Stewart (2011).