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.TH ereduc G "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
ereduc - computes matrix column echelon form by qz transformations
.SH CALLING SEQUENCE
.nf
[E,Q,Z [,stair [,rk]]]=ereduc(X,tol)
.fi
.SH PARAMETERS
.TP
X
: m x n matrix with real entries.
.TP
tol
: real positive scalar.
.TP
E
: column echelon form matrix
.TP
Q
: m x m unitary matrix
.TP
Z
: n x n unitary matrix
.TP
stair
: vector of indexes,
.RS
.TP
*
\fVISTAIR(i) = + j \fR if the boundary element \fVE(i,j)\fR is a
corner point.
.TP
*
\fVISTAIR(i) = - j\fR if the boundary element \fVE(i,j)\fR is not
a corner point.
.RE
\fV(i=1,...,M)\fR
.TP
rk
: integer, estimated rank of the matrix
.SH DESCRIPTION
Given an \fVm x n\fR matrix \fVX\fR (not necessarily regular) the function
ereduc computes a unitary transformed matrix \fVE=Q*X*Z\fR which is in
column echelon form (trapezoidal form). Furthermore the rank of
matrix \fVX\fR is determined.
.SH EXAMPLE
.nf
X=[1 2 3;4 5 6]
[E,Q,Z ,stair ,rk]=ereduc(X,1.d-15)
.fi
.SH SEE ALSO
fstair
.SH AUTHOR
Th.G.J. Beelen (Philips Glass Eindhoven). SLICOT
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