An upper bound for the condition number of a matrix in spectral norm

In this note we generalize an upper bound given in Guggenheimer et al. (College Math. J. 26(1) (1995) 2) for the condition number of a matrix as a function of the determinant, the Frobenius norm and of k singular values. If no singular value is known it is possible to derive an upper bound for the condition number applying lower and upper bounds for the product of a subset of singular values.