When describing the condition number of a correlation matrix I have seen is described as the ratio of the singular values (from singluar value decomposition).
I have also seen it described as the ratio of the eigenvalues (from PCA analysis).
Can both be correct (under say different norms)? If so which one would be considered standard?
For a symmetric positive semi-definite matrix the definitions are equivalent since singular values are eigenvalues.
The computation of eigenvalues is expensive, so often a condition number is defined as norm of matrix $A$ times the corresponding norm of the inverse. Thus a wide variety of definitions may be encountered. The operator norm of a matrix induced by Euclidean (sum-of-squares) vector norms will give the condition number defined as above, a ratio of largest to smallest singular values.