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