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.
Dimension: matrix
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.
Type: double
Dimension: scalar

Outputs

R
The column space basis. Also called the range.
Type: double

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.