What is the significance/geometric interpretation of eigen values or eigen vectors in a vector space?

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  • We like to reduce transformations to combinations of simpler ones. A very simple kind of transformation is a dilation. We can often reduce a linear transformation to dilations to different extents along different directions. This is called diagonalization (strictly speaking, diagonalization over the real numbers). With a bit more work, we can also make eigenvalues tell us about rotation. What they cannot really tell us about is shear. – Ian Nov 04 '15 at 05:05
  • There is definitely an old question about this somewhere on the site with plenty of good answers. – Ben Grossmann Nov 04 '15 at 05:20
  • [here it is](http://math.stackexchange.com/questions/243533/how-to-intuitively-understand-eigenvalue-and-eigenvector) – Ben Grossmann Nov 04 '15 at 05:22
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    actually I was [thinking of this one](http://math.stackexchange.com/questions/23312/what-is-the-importance-of-eigenvalues-eigenvectors) – Ben Grossmann Nov 04 '15 at 05:24

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