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Understanding "Eigenvalues" with the Mona Lisa

Last updated at Posted at 2022-09-20

Linear transformation of a Mona Lisa image into a parallelogram.

From the left image to the right.

In this linear transformation, the right-pointing arrow (blue) in the image remains unchanged, whereas the
The upward pointing arrow (red) has changed direction.

The blue arrow is the eigenvector of this transformation
The red arrow is not an eigenvector.

Here the blue arrow is neither stretched nor constricted, so its eigenvalue is 1.
All vectors parallel to this vector are eigenvectors.
These vectors, including the zero vector, form the eigenspace for this eigenvalue.


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