Scilab Function
Last update : 00/00/0000

range - range (span) of A^k

Calling Sequence

[U,dim]=range(A,k)

Parameters

Description

Computation of Range A^k : the first dim columns of U' span the range of A^k. U performs a row compression of A^k without calculating A^k.Vector y belongs to range A^k iff the last components of U*y are zeros (i.e. numerically small). U*U' is the Identity matrix

Examples

    
    A=rand(4,2)*rand(2,4);   // 4 column vectors, 2 independent.
    [U,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(U(dim+1:$,:)*y1)    //the last entries are zeros, y1 is in the range of A
    norm(U(dim+1:$,:)*y2)    //the last entries are not zeros

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

    norm(I*coeffs-y1)        //check

    
  

See Also

fullrfk,  rowcomp,  orth,  

Author

F. D. INRIA ;

Used Function

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