Please consider the snippet below out of Bishop's book on PRML.

According to my understanding of an ellipse, the radii are $\sqrt\lambda_{1}$ along the horizontal axis ($w_1$) and $\sqrt\lambda_{2}$ along the vertical axis ($w_2$).

When looking at Fig. 3.15, the radius along the $w_1$-axis is larger than the radius along the $w_2$-axis.

Therefore, I would say that $\lambda_{1}$ is larger than $\lambda_{2}$

The text in Section 3.5.3, however, claims the opposite. Where did I make an error?

Thanks for any pointers or clarifications!

• Your question is vague, because it lacks any account of what the $\lambda_i$ are, but I suspect the key to understanding the text is the word "contours." Consider, for instance, contours (aka "level sets") of the function $x^2 + 2y^2$ in the $x,y$ plane. They are ellipses--with the smaller axes in the vertical direction because the coefficient of $y$ is greater than that of $x$. – whuber Aug 27 '17 at 20:48