linsolve

linsolve

linsolve — linear equation solver

Calling sequence

[x0,kerA]=linsolve(A,b [,x0])

Parameters

`A`	: a `na x ma` real matrix (possibly sparse)
`b`	: a `na x 1` vector (same row dimension as `A`)
`x0`	: a real vector
`kerA`	: a `ma x k` real matrix

Description

linsolve computes all the solutions to A*x+b=0.

x0 is a particular solution (if any) and kerA= nullspace of A. Any x=x0+kerA*w with arbitrary w satisfies A*x+b=0.

If compatible x0 is given on entry, x0 is returned. If not a compatible x0, if any, is returned.

Examples



A=rand(5,3)*rand(3,8);
b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b   //compatible b
b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b   //uncompatible b
A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b  //x is unique

See also

inv, pinv, colcomp, im_inv