Parameters

Description

Row compression of A. Ac = W*A is a row compressed matrix: i.e. Ac=[Af;0] with Af full row rank.

flag and tol are optional parameters: flag='qr' or 'svd' (default 'svd').

tol is a tolerance parameter.

The rk first columns of W' span the range of A.

The rk first (top) rows of W span the row range of A.

A non zero vector x belongs to range(A) iff W*x is row compressed in accordance with Ac i.e the norm of its last components is small w.r.t its first components.

Examples

    
    A=rand(5,2)*rand(2,4);              // 4 col. vectors, 2 independent.
    [X,dim]=rowcomp(A);Xp=X';
    svd([Xp(:,1:dim),A])                //span(A) = span(Xp(:,1:dim)
    x=A*rand(4,1);                      //x belongs to span(A)
    y=X*x  
    norm(y(dim+1:$))/norm(y(1:dim))     // small
    
  

See Also

Authors

F. D.; INRIA

Used Functions

The rowcomp function is based on the svd or qr decompositions.