How to find the condition number of a 3*3 matrix with singular value 10, 1 and 1/10?

Question

If the singular values of a 3*3 matrix are 10, 1 and 1/10 respectively, what is the condition number of the matrix? Is such a matrix numerically tractable?

Answer 1

The condition number of a matrix is equal to ||A||*||A^-1||; that is, the product of its operator norm and the operator norm of its inverse. Note that ||A|| = largest singular value of A (which is 10 in this problem). Thus, the largest singular value of A^-1 is 1/(1/10) = 10, as well.

So, k(A) = 10*10 = 100 is the condition number. Now, based on this, judge whether the matrix is numerically tractable.