Section: Array Generation and Manipulations
y = cond(A)
where A is a matrix. If you want to compute the condition number in a different norm (e.g., the 1-norm), 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 1-norm, or the max column sum of A
p = 2
returns the 2-norm (largest singular value of A)
p = inf
returns the infinity norm, or the max row sum of A
p = 'fro'
returns the Frobenius-norm (vector Euclidean norm, or RMS value)
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.
--> A = [1,1;0,1e-15] A = 1.0000 1.0000 0 0.0000 --> cond(A) ans = 2000000000000000 --> cond(A,1) ans = 2000000000000002 --> quit
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 --> quit