Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange
Please login or create an account
Change language to: English - Français - Português - 日本語

Please note that the recommended version of Scilab is 6.0.0. This page might be outdated.
See the recommended documentation of this function

Справка Scilab >> 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

See Also

  • 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.

Scilab Enterprises
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Thu Oct 02 14:01:04 CEST 2014