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# ereduc

computes matrix column echelon form by qz transformations

### Syntax

`[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)```