spanplus

Arguments

A, B

two real or complex matrices with equal number of rows

X

orthogonal or unitary square matrix

dim, dima

integers, dimension of subspaces

tol

nonnegative real number

Description

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).

Examples

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

See also

• spaninter — subspace intersection
• im_inv — inverse image
• spantwo — sum and intersection of subspaces