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Справка Scilab >> Linear Algebra > Subspaces > spanplus

# spanplus

sum of subspaces

### Calling Sequence

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

### 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```