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# 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

## Comments

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