finds an x that solves the matrix equation m.x==b.
Details and Options
- LinearSolve works on both numerical and symbolic matrices, as well as SparseArray objects.
- The argument b can be either a vector or a matrix. »
- The matrix m can be square or rectangular. »
- LinearSolve[m] and LinearSolveFunction[…] provide an efficient way to solve the same approximate numerical linear system many times.
- LinearSolve[m,b] is equivalent to LinearSolve[m][b].
- For underdetermined systems, LinearSolve will return one of the possible solutions; Solve will return a general solution. »
- LinearSolve has the following options and settings:
Method Automatic method to use Modulus 0 whether to solve modulo n ZeroTest Automatic test to determine when expressions are zero
- The ZeroTest option only applies to exact and symbolic matrices.
- With Method->Automatic, the method is automatically selected depending upon input.
- Explicit Method settings for exact and symbolic matrices include:
"CofactorExpansion" Laplace cofactor expansion "DivisionFreeRowReduction" Bareiss method of division-free row reduction "OneStepRowReduction" standard row reduction
- Explicit Method settings for approximate numeric matrices include:
"Banded" banded matrix solver "Cholesky" Cholesky method for positive definite Hermitian matrices "Krylov" iterative Krylov sparse solver "Multifrontal" direct sparse LU decomposition
Examplesopen allclose all
Basic Examples (2)
With no right‐hand side, a LinearSolveFunction is returned:
Properties & Relations (4)
Possible Issues (2)
Neat Examples (3)
Introduced in 1988
(1.0)| Updated in 2014