Solving equations with singular matrix

[Zak]

Hi!

I have a problem: I need to solve an equation, Ax=y, where A is a known matrix, y is a known column vector and x is an unknown column vector. Unfortunately, A is singular so I cannot do the simple solution of inverse(A)*y=x. Does anybody know of any way that I can obtain the coefficients for x?

Thanks in advance

 

[Paul Colby]

You could look at SVD (singular Value Decomposition). It's covered very nicely in Strang's book

 

[jasonRF]

If A is singular then Ax=y either has no solution (eg if y is not in the column space of A) or an infinite number of solutions (can add any solution of Ax=0). So you need to figure out what case you have, and what you want to do. If there are infinite solutions, which one do you want? If there is no solution, what do you mean by "solve?"

jason