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public class LUDecompositionextends Objectimplements SerializableFor an m x n matrix A with m >= n, the LU decomposition is an m x nunit lower triangular matrix L, an n x n upper triangular matrix U,and a permutation vector piv of length m so that A(piv,:) = L*U;If m < n, then L is m x m and U is m x n.
The LU decomposition with pivoting always exists, even if the matrix issingular, so the constructor will never fail. The primary use of theLU decomposition is in the solution of square systems of simultaneouslinear equations. This will fail if isNonsingular() returns false.
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