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rowcomp(1) Scilab Function rowcomp(1)
NAME
rowcomp - row compression, range
CALLING SEQUENCE
[W,rk]=rowcomp(A [,flag] [,tol])
PARAMETERS
A : real or complex matrix
flag : character string
tol : real number
W : square non-singular matrix (change of basis)
rk : integer (rank of A)
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 (of order sqrt(%eps) as default value).
The rk first columns of W' span the range of A.
The rk first (top) rows of W span the row range of A.
Remark
A non zero vector x belongs to range(A) iff W*x is row compressed in accor-
dance with Ac i.e the norm of its last components is small w.r.t its first
components.
EXAMPLE
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
colcomp, fullrf, fullrfk
AUTHOR
F. D.
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