Matrix decomposition: Difference between revisions

Revision as of 11:40, 12 January 2021

Revision as of 22:48, 25 January 2021

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{{Distinguish|Matrixmatrix factorization of a polynomial}}
{{Short description|Representation of a matrix as a product}}

In the [[mathematics|mathematical]] discipline of [[linear algebra]], a '''matrix decomposition''' or '''matrix factorization''' is a [[factorization]] of a [[Matrix (mathematics)|matrix]] into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.

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These factorizations are based on early work by {{harvtxt|Fredholm|1903}}, {{harvtxt|Hilbert|1904}} and {{harvtxt|Schmidt|1907}}. For an account, and a translation to English of the seminal papers, see {{harvtxt|Stewart|2011}}.

== See also ==

* [[Matrix splitting]]

* [[Non-negative matrix factorization]]

* [[Principal component analysis]]

== Notes ==

{{reflist}}

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*{{citation|last=Townsend|first=A.|last2=Trefethen|first2=L. N.|year=2015|title=Continuous analogues of matrix factorizations|journal=[[Proceedings of the Royal Society|Proc. R. Soc. A]]|volume=471|issue=2173|pages=20140585|doi=10.1098/rspa.2014.0585|pmid=25568618|pmc=4277194|bibcode=2014RSPSA.47140585T}}

== External links ==

*[http://www.bluebit.gr/matrix-calculator/ Online Matrix Calculator]

*[http://www.wolframalpha.com/input/?i=matrix+decomposition&rawformassumption={%22C%22,+%22matrix+decomposition%22}+-%3E+{%22Calculator%22}&rawformassumption={%22MC%22,%22%22}-%3E{%22Formula%22} Wolfram Alpha Matrix Decomposition Computation » LU and QR Decomposition]

*[http://eom.springer.de/M/m120140.htm Springer Encyclopaedia of Mathematics » Matrix factorization]

* [https://web.archive.org/web/20110314171151/http://www.graphlab.ml.cmu.edu/pmf.html GraphLab] [[GraphLab]] collaborative filtering library, large scale parallel implementation of matrix decomposition methods (in C++) for multicore.

{{linear algebra}}