Understanding eigenvectors and eigenvalues

“Eigen” is the German word for “own” and can also mean “characteristic” or “proper.” An eigenvector is like an arrow in space that doesn’t change its direction when you apply a transformation to it, such as stretching or squishing. Imagine you have a rubber band (the eigenvector) and you stretch it or squish it using a magic machine (the transformation). If the rubber band still points in the same direction after the magic, it’s an eigenvector. These special arrows are really helpful in math and science to understand how things change and stay the same in different situations. Refer to Figure 4.6 for more information on this particular property, and then I will introduce the mathematical properties. The left image (A) in Figure 4.6 is a 2D image. After we apply a transformation to this image, it becomes the right image (B). Note that the vertical axis (yellow vector) does...