I have the daunting task of explaining the concept of Eigenvalue to biologists and physicians with minimal mathematical background in a very short seminar. Any ideas on how to approach the task or introducing resources that might have already addressed that, is much appreciated.
Thanks!
I found the question interesting, though I know little about it. A simple Google search will turn up dozens of nice diagrams and explanations.
The typical "first example" in introductory math books was often to consider how a real matrix maps a unit sphere (or circle in R2), observe that it is an ellipse, and then realize that the lengths and directions of the semiaxes corresponded to the eigenvalues and eigenvectors, respectively. This is perhaps not the most inspired or original approach, but it might at least showcase in a conveniently geometric fashion how eigenvectors are kind of magic directions for an operator, along which its action reduces simply to a multiplication by a scalar.
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