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For exam preperation I want to know how to get an intuition to draw in the eigenvectors corresponding to the smallest and largest eigenvalue. Student friends say "just get the direction of the largest variance" but I don't quite get it still.

For example for this plot enter image description here

the first Eigenvector is from the bottom left to the upper right. How would the Eigenvector corresponding to the smallest Eigenvalue look like?

And on the other hand for this plot:

enter image description here

It is (instead of a horizontal line between the both class, which would be my inutitive solution) a line which is horizontal but slightly tilted. How do I get an intuition for this?

MagikarpSama
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  • This might be relevant https://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues – User2321 Jul 31 '19 at 13:22
  • I would strongly refer you to this answer: https://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues It has been extremely helpful to me. Another useful resource might be this one: [HERE](http://setosa.io/ev/eigenvectors-and-eigenvalues/) – StoryTeller0815 Jul 31 '19 at 13:37

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