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I am doing my PhD in Informatics and especially graph theory. I came across eigen-analysis numerous times in the context of spectral graph theory.

The question:

I would like to see an *elegant geometric explanation* of the eigenvalues and eigenvectors of a Matrix A (symmetric, real, >= 0). (Suppose that the only thing I know about linear algebra is how to change between bases and do a few matrix operations)

Of course I have looked many textbooks, but they only write math, not essence.

thanks!

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# Eigen-analysis insight

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