generates a representation of the LU decomposition of a square matrix m.
Details and Options
- LUDecomposition returns a list of three elements. The first element is a combination of upper‐ and lower‐triangular matrices, the second element is a vector specifying rows used for pivoting, and for approximate numerical matrices m the third element is an estimate of the L∞ condition number of m.
Examplesopen allclose all
Basic Examples (1)
Illustrate the structure by using MatrixPlot:
LinearSolve[m] sets up an LU decomposition in a functional form convenient for solving:
This can be done manually with the output of LUDecomposition as well:
Wolfram Research (1996), LUDecomposition, Wolfram Language function, https://reference.wolfram.com/language/ref/LUDecomposition.html.
Wolfram Language. 1996. "LUDecomposition." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LUDecomposition.html.
Wolfram Language. (1996). LUDecomposition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LUDecomposition.html