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Scilab help >> Linear Algebra > Kernel > range

# range

range (span) of A^k

### Calling Sequence

`[X,dim]=range(A,k)`

### Arguments

A

real square matrix

k

integer

X

orthonormal real matrix

dim

integer (dimension of subspace)

### Description

Computation of Range `A^k` ; the first dim rows of `X` span the range of `A^k`. The last rows of `X` span the orthogonal complement of the range. `X*X'` is the Identity matrix

### Examples

```A=rand(4,2)*rand(2,4);   // 4 column vectors, 2 independent.
[X,dim]=range(A,1);dim   // compute the range

y1=A*rand(4,1);          //a vector which is in the range of A
y2=rand(4,1);            //a vector which is not  in the range of A
norm(X(dim+1:\$,:)*y1)    //the last entries are zeros, y1 is in the range of A
norm(X(dim+1:\$,:)*y2)    //the last entries are not zeros

I=X(1:dim,:)'            //I is a basis of the range
coeffs=X(1:dim,:)*y1     // components of y1 relative to the I basis

norm(I*coeffs-y1)        //check```

• fullrfk — full rank factorization of A^k
• rowcomp — row compression, range

### Used Functions

The `range` function is based on the rowcomp function which uses the svd decomposition.

 Report an issue << kernel Kernel rowcomp >>

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