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== Decompositions related to solving systems of linear equations ==
=== LU decomposition ===
{{main|LU decomposition}}
*Traditionally applicable to: [[square matrix]] ''A'', although rectangular matrices can be applicable.<ref>{{Cite book|last=Lay|first=David C.|url=https://www.worldcat.org/oclc/920463015|title=Linear algebra and its applications|date=2016|others=Steven R. Lay, Judith McDonald|isbn=1-292-09223-8|edition=Fifth Global|___location=Harlow|pages=142|oclc=920463015}}</ref><ref group="nb">If a non-square matrix is used, however, then the matrix ''U'' will also have the same rectangular shape as the original matrix ''A''. And so, calling the matrix ''U'' would be incorrect as the correct term would be that ''U'' is the 'row echelon form' of ''A''. Other than this, there are no differences in LU factorization for square and non-square matrices.</ref>
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