# cond¶

## Purpose¶

Computes the condition number of a matrix using the singular value decomposition.

## Format¶

c = cond(x)
Parameters

x (NxK matrix) – used to compute condition number

Returns

c (scalar) – an estimate of the condition number of x. This equals the ratio of the largest singular value to the smallest. If the smallest singular value is zero or not all of the singular values can be computed, the return value is 1e300.

## Examples¶

### Basic usage¶

x = { 4 2 6,
8 5 7,
3 8 9 };

c = cond(x);


will assign c to equal:

c = 9.8436943


### Decrease condition number by standardizing variables¶

// Set seed for repeatable random numbers
rndseed 777;

X = rndn(100, 3) ~ rndi(100, 1);

print "cond(X)   = " cond(X);

// Create standardized X
X_s = X - meanc(X)';
X_s = X_s ./ stdc(X_s)';

print "cond(X_s) = " cond(X_s);


will create the following output:

cond(X)   =    2.7008906e+09
cond(X_s) =        1.2504154