im_inv - inverse image
i.e vectors whose image through A are in range(B)
The dim first columns of X span
tol is a threshold used to test if subspace inclusion; default value is tol = 100*%eps. If Y is returned, then [Y*A*X,Y*B] is partitioned as follows:
where B1 has full row rank (equals rank(B)) and A22 has full column rank and has dim columns.
A=[rand(2,5);[zeros(3,4),rand(3,1)]];B=[[1,1;1,1];zeros(3,2)]; W=rand(5,5);A=W*A;B=W*B; [X,dim]=im_inv(A,B) svd([A*X(:,1:dim),B]) //vectors A*X(:,1:dim) belong to range(B) [X,dim,Y]=im_inv(A,B);[Y*A*X,Y*B]