• LinearSolve[m, b] finds an x which solves the matrix equation m.xb.
• LinearSolve[m] generates a LinearSolveFunction[ ... ] which can be applied repeatedly to different b.
works on both numerical and symbolic matrices, as well as SparseArray
• 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[m, b, Modulus -> n] takes the matrix equation to be modulo n.
• LinearSolve[m, b, ZeroTest -> test]
evaluates test[ m[[i, j]] ]
to determine whether matrix elements are zero. The default setting is ZeroTest -> (# 0 &)
• A Method
option can also be given. Settings for exact and symbolic matrices include "CofactorExpansion"
. Settings for approximate numerical matrices include "Cholesky"
, and for sparse arrays "Multifrontal"
. The default setting of Automatic
switches between these methods depending on the matrix given.
• New in Version 1; modified in 5.
• Advanced Documentation.