finds an x that solves the matrix equation m.x==b.
- 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
Introduced in 1988
(1.0)| Updated in 2014