computes matrix column echelon form by qz transformations
[E,Q,Z [,stair [,rk]]]=ereduc(X,tol)
m x n matrix with real entries.
real positive scalar.
column echelon form matrix
m x m unitary matrix
n x n unitary matrix
vector of indexes,
ISTAIR(i) = + j
if the boundary element E(i,j)
is a corner point.
ISTAIR(i) = - j
if the boundary element E(i,j)
is not a corner point.
(i=1,...,M)
integer, estimated rank of the matrix
Given an m x n
matrix X
(not necessarily regular) the function
ereduc computes a unitary transformed matrix E=Q*X*Z
which is in
column echelon form (trapezoidal form). Furthermore the rank of
matrix X
is determined.