# Ratio of eigenvalues as the condition number of a matrix

I'm having an issue with a 2x2 matrix. My understanding is that one could use the ratio of the maximum eigenvalue to the minimum eigenvalue of a matrix in order to determine the condition number, however I can't seem to get this to work.

$$\begin {matrix} 1.73 & 0.25\\ -1 & 0.43 \end {matrix}$$

I get that the eigenvalues of this matrix are 1.4953 and 0.66467, however dividing these two yields 2.25 as the result. According to my prof's notes the condition number of this matrix is 4 not 2.25...

I'd really appreciate it if someone could clear this up for me.

$\kappa_2(A) = |\sigma_{\max}|/|\sigma_{\min}|$, your formula only holds if $A$ is normal. In this case we have that $\sigma_{\max} = 1.9896$ and $\sigma_{\min} = 0.4974$ and $$\dfrac{1.9896}{0.4974} \approx 4$$