# orth

Range space of a matrix.

## Syntax

* O = orth(A)
* O = orth(A, tol)

## Input argument

* A - Input matrix
* tol - a numeric value: scalar, singular value tolerance

## Output argument

* O - real or complex number (double or single).

## Description

**O = orth(A)** returns an orthonormal basis for the range of **A**.

## Example

```matlab
M = [10 -20 40; -50 20 0; 10 0 30]
O = orth(M)
```

## See also

[svd](svd), [rank](rank).

## History

| Version | Description     |
| ------- | --------------- |
| 1.0.0   | initial version |

## Author

Allan CORNET
