spanplus

Scilab Function
Last update : April 1993

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

### See Also

`spaninter` , `im_inv` , `spantwo` ,

### Author

F. D.; ;