spanplus

spanplus — sum of subspaces

Calling sequence

[X,dim,dima]=spanplus(A,B[,tol])

Parameters

`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

Author

F. D.; ;