COND Condition Number of a Matrix
Section: Array Generation and Manipulations
Usage
Calculates the condition number of a matrix. To compute the 2norm condition number of a matrix (ratio of largest to smallest singular values), use the syntaxy = cond(A)
where A is a matrix. If you want to compute the condition number in a different norm (e.g., the 1norm), use the second syntax
y = cond(A,p)
where p
is the norm to use when computing the condition number.
The following choices of p
are supported

p = 1
returns the 1norm, or the max column sum of A 
p = 2
returns the 2norm (largest singular value of A) 
p = inf
returns the infinity norm, or the max row sum of A 
p = 'fro'
returns the Frobeniusnorm (vector Euclidean norm, or RMS value)
Function Internals
The condition number is defined as
This equation is precisely how the condition number is computed for
the case p ~= 2
. For the p=2
case, the condition number can
be computed much more efficiently using the ratio of the largest and
smallest singular values.
Example
The condition number of this matrix is large> A = [1,1;0,1e15] A = 1.0000 1.0000 0 0.0000 > cond(A) ans = 2000000000000000 > cond(A,1) ans = 2000000000000002
You can also (for the case p=1
use rcond
to calculate an estimate
of the condition number
> 1/rcond(A) ans = 2.0000e+15