Scilab 5.5.2
Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
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
Used Functions
The range
function is based on the rowcomp function
which uses the svd decomposition.
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