# orth

Compute an orthonormal basis for the column space of a matrix.

## Syntax

R = orth(A)

R = orth(A, tol)

## Inputs

`A`- The matrix whose column space basis computed.
`tol`- A threshold for rounding off near-zero singular values. The default is the product of max(size(A)), the largest singular value, and eps.

## Outputs

- R
- The column space basis. Also called the range.

## Example

Matrix input with default
tolerance:

```
A = [1,2,3,4;5,6,7,8;9,10,11,12;13,14,15,16];
R = orth(A)
```

```
R = [Matrix] 4 x 2
0.13472 0.82574
0.34076 0.42882
0.54679 0.03189
0.75283 -0.36503
```

## Comments

The column space basis is not unique.