I want to solve the following system of equations using SVD:
S = AX,
where S is a 40x1 matrix (rows x columns), A is 40x3 and X is 3x1 matrix contains the unknowns.
I found the svd Matlab function which I want to use but I am not sure how to obtain the values of X after performing the SVD.
I found the SVD of the matrix A as follows:
[U,S,V] = svd(A);
U is a 40x40 matrix. S is a 40x3 matrix. V is a 3x3 matrix.
I have to use U, S and V to derive the solutions of X but I don't understand how.
Can anyone help with that?
I have read that for an mxn matrix A there exists: an mxn orthogonal matrix U, an nxn diagonal matrix S an nxn orthogonal matrix V
such that A=U*S*transpose(V).
After using the svd in Matlab the outputs U,S,V have different dimensions from what I've read in the literature. I don't understand why though. Thank you.