Eli5: what are eigen values and eigen vectors and how is it useful.
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A very intuitive explanation of one application of eigenvalues and eigenvectors:
Eigenvectors “point” in the same direction as most of your data, and eigenvalues tell you how strongly your data points that direction.
For example let’s say I have a point cloud in the shape of a book like the green image here: https://www.semanticscholar.org/paper/Tutorial%3A-Point-Cloud-Library%3A-Three-Dimensional-6-Aldoma-M%C3%A1rton/53f85aa476673f50c7a4c255c46cde461d3ba949/figure/0
The eigenvectors of this data (generally) will point in the same direction as the faces of the book as shown on the picture. The largest eigenvalue will correspond to the up direction because the book is longest in that direction. The second eigenvalue will correspond to the left direction, and smallest eigenvalue to the right/coming out the face.
This is helpful because it works even if I don’t know the original orientation of the book.
See more at the page on Principle Component Analysis: https://en.wikipedia.org/wiki/Principal_component_analysis?wprov=sfla1
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