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# rowcomp

row compression, range

### Syntax

[W,rk]=rowcomp(A [,flag [,tol]])

### Arguments

- A
real or complex matrix

- flag
optional character string, with possible values

`'svd'`

or`'qr'`

. The default value is`'svd'`

.- tol
optional real non negative number. The default value is

`sqrt(%eps)*norm(A,1)`

.- W
square non-singular matrix (change of basis)

- rk
integer (rank of

`A`

)

### Description

Row compression of `A`

. `Ac = W*A`

is a row compressed matrix: i.e.
`Ac=[Af;0]`

with `Af`

full row rank.

`flag`

and `tol`

are optional parameters: `flag='qr'`

or `'svd'`

(default `'svd'`

).

`tol`

is a tolerance parameter.

The `rk`

first columns of `W'`

span the range of
`A`

.

The `rk`

first (top) rows of `W`

span the row
range of `A`

.

A non zero vector `x`

belongs to range(`A`

) iff
`W*x`

is row compressed in accordance with `Ac`

i.e the norm of its last components is small w.r.t its first
components.

## Comments

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