U:RDoc::NormalClass[iI"LUPDecomposition:ETI"Matrix::LUPDecomposition;TI"Object;To:RDoc::Markup::Document:@parts[o;;[o:RDoc::Markup::Paragraph;[	I"KFor an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n ;TI"Junit lower triangular matrix L, an n-by-n upper triangular matrix U, ;TI":and a m-by-m permutation matrix P so that L*U = P*A. ;TI"0If m < n, then L is m-by-m and U is m-by-n.;To:RDoc::Markup::BlankLineo;	;[	I"NThe LUP decomposition with pivoting always exists, even if the matrix is ;TI"Ksingular, so the constructor will never fail.  The primary use of the ;TI"KLU decomposition is in the solution of square systems of simultaneous ;TI"Alinear equations.  This will fail if singular? returns true.;T:
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