What exactly is antieigenvalue analysis?

Solution 1:

I'm very interested in this.

My intuitive take is that normal eigenvalues are those vectors associated with a linear transformation that undergo no rotation or sheer, and are scalar multiples of direction of the transformation.

If I imagine a field of randomly pointing vectors (like flags without wind) and then apply a transformation, the anti-eigenvectors are those vectors that undergo MAXIMUM rotation under the transformation.

It's actually more interesting in some ways than eigenvectors which get all the airtime in linear algebra. Because one might also (practically and intuitively) want to know the set of vectors that undergo maximum deformation or rotation under a transformation. That's where a lot of the "work" of the transform is happening.