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

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  • $\begingroup$ 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. $\endgroup$ – Ian Nov 4 '15 at 5:05
  • $\begingroup$ There is definitely an old question about this somewhere on the site with plenty of good answers. $\endgroup$ – Ben Grossmann Nov 4 '15 at 5:20
  • $\begingroup$ here it is $\endgroup$ – Ben Grossmann Nov 4 '15 at 5:22
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    $\begingroup$ actually I was thinking of this one $\endgroup$ – Ben Grossmann Nov 4 '15 at 5:24