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Aide de Scilab >> Algèbre Lineaire > Sous-espaces vectoriels > spaninter

# spaninter

subspace intersection

### Syntax

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

### Arguments

A, B

two real or complex matrices with equal number of rows

X

orthogonal or unitary square matrix

dim

integer, dimension of subspace range(`A`) inter range(`B`)

### Description

computes the intersection of range(`A`) and range(`B`).

The first `dim` columns of `X` span this intersection i.e. `X(:,1:dim)` is an orthogonal basis for

range(`A`) inter range(`B`)

In the `X` basis `A` and `B` are respectively represented by:

`X'*A` and `X'*B`.

`tol` is a threshold (`sqrt(%eps)` is the default value).

### Examples

```A=rand(5,3)*rand(3,4);     // A is 5 x 4, rank=3
B=[A(:,2),rand(5,1)]*rand(2,2);
[X,dim]=spaninter(A,B);
X1=X(:,1:dim);    //The intersection
svd(A),svd([X1,A])   // X1 in span(A)
svd(B),svd([B,X1])   // X1 in span(B)```

### See also

• spanplus — sum of subspaces
• spantwo — sum and intersection of subspaces

### Comments

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