COND Condition Number of a Matrix
Section: Array Generation and Manipulations
Usage
Calculates the condition number of a matrix. To compute the 2-norm 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 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 = 1returns the 1-norm, or the max column sum of A -
p = 2returns the 2-norm (largest singular value of A) -
p = infreturns the infinity norm, or the max row sum of A -
p = 'fro'returns the Frobenius-norm (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;0,1e-15]
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