spanplus - sum of subspaces
computes a basis X such that:
the first dima columns of X span Range( A ) and the following ( dim-dima ) columns make a basis of A+B relative to A .
The dim first columns of X make a basis for A+B .
One has the following canonical form for [A,B] :
[*,*] (dima rows) X'*[A,B]=[0,*] (dim-dima rows) [0,0]
tol is an optional argument (see function code).
A=rand(6,2)*rand(2,5); // rank(A)=2 B=[A(:,1),rand(6,2)]*rand(3,3); //two additional independent vectors [X,dim,dimA]=spanplus(A,B); dimA dim
spaninter , im_inv , spantwo ,
F. D.; ;