# orth¶

## Purpose¶

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

## Format¶

y = orth(x)
Parameters

x (NxK matrix) – data

Returns

y (NxL matrix) – such that $$y'y = eye(L)$$ and whose columns span the same space as the columns of x; L is the rank of x.

## Global Input¶

_orthol

(scalar), the tolerance for testing if diagonal elements are approaching zero. The default is 1.0e-14.

## Examples¶

x = { 6 5 4,
2 7 5 };

y = orth(x);


After the code above:

y = -0.58123819      -0.81373347    y'y = 1  0
-0.81373347       0.58123819          0  1


qqr.src