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Scilab help >> Linear Algebra > Kernel > rowcomp


row compression, range

Calling Sequence

[W,rk]=rowcomp(A [,flag [,tol]])



real or complex matrix


optional character string, with possible values 'svd' or 'qr'. The default value is 'svd'.


optional real non negative number. The default value is sqrt(%eps)*norm(A,1).


square non-singular matrix (change of basis)


integer (rank of A)


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.


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

See Also

  • colcomp — column compression, kernel, nullspace
  • fullrf — full rank factorization
  • fullrfk — full rank factorization of A^k

Used Functions

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

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Last updated:
Tue Apr 02 17:36:21 CEST 2013