Name

ereduc — computes matrix column echelon form by qz transformations

Calling Sequence

[E,Q,Z [,stair [,rk]]]=ereduc(X,tol)

Parameters

X

m x n matrix with real entries.

tol

real positive scalar.

E

column echelon form matrix

Q

m x m unitary matrix

Z

n x n unitary matrix

stair

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)

rk

integer, estimated rank of the matrix

Description

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.

Examples

 
X=[1 2 3;4 5 6]
[E,Q,Z ,stair ,rk]=ereduc(X,1.d-15)

See Also

fstair

Authors

Th.G.J. Beelen (Philips Glass Eindhoven). SLICOT