According to https://en.wikipedia.org/wiki/Condition_number, the conditional number for the matrix $M$ is $||A|| \times ||A^{-1}|| = ||A A^{-1}|| = 1$. In another word, is $||A||$ the absolute value of the determinant $|A|$ in the above definition?
I have manually tested a few $||A|| \times ||A^{-1}||$ including Helbert matrices and they are all 1.
What is wrong?
Ah! $||A||$ is the matrix norm defined as https://en.wikipedia.org/wiki/Matrix_norm