ereduc

computes matrix column echelon form by qz transformations

Calling Sequence

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

Arguments

: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 computes pencil column echelon form by qz transformations