![]() Diseases tend to spread slowly, heat spreads gradually, and vibrations propagate gradually. In the case of nonlinear mappings, the fixed points in the eigenvector matrix would be replaced with functions that can take on many different values.Įigenvectors pop up in the study of the spread of infectious diseases or vibration studies or heat transfer because these are generally linear functions. So eigenvectors do well with linear mappings, but not with nonlinear mappings. If the mapping isn't linear, we're out of the realm of the eigenvector and into the realm of the tensor. You can capture the process of doing this in a matrix, and that matrix represents a vector that's called the eigenvector. ![]() That is, a set of points (the painting) gets transformed by multiplying the x distance by one value and the y value by a different value. A change in perspective in a painting is really just a vector transformation that performs a linear map. ![]() Objects appear distorted and foreshortened. This would represent what happens if you look a a scene from close to the ground as opposed to higher in the air. If you scale the x direction to a different value than the y direction (say x -> 3x while y -> 2y), you simulate a change of perspective. Let's take an example: suppose you want to change the perspective of a painting. Eigenvalues and eigenvectors prove enormously useful in linear mapping.
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