Re: The Condition Number of a Matrix Message #2 Posted by Jeff Kearns on 8 Feb 2012, 2:48 p.m., in response to message #1 by Namir
Condition Number
is defined as the product of the norm of A and the norm of Ainverse.
If we use the usual Euclidean norm on vectors and the associated matrix norm, then the condition number is the ratio of the largest singular value of matrix A to the smallest. (Singular values are computed by process called SVD  Singular Value Decomposition and in Matlab the calculation is simply invoked by command svd).
Condition number depends on the underlying norm. However, regardless of the norm, it is always greater or equal to 1. If it is close to one, the matrix is well conditioned which means its inverse can be computed with good accuracy. If the condition number is large, then the matrix is said to be illconditioned. Practically, such a matrix is almost singular, and the computation of its inverse, or solution of a linear system of equations is prone to large numerical errors. A matrix that is not invertible has the condition number equal to infinity.
