Eigenvalues and Eigenvectors

In linear algebra, an eigenvector of a linear transformation is a nonzero vector whose direction is left unchanged, or exactly reversed, by that transformation; the corresponding eigenvalue is the factor by which the eigenvector is scaled, which may be negative or complex. Geometrically, a linear transformation's eigenvectors are the vectors that are only stretched or shrunk, never rotated or sheared, by the transformation. Eigenvalues and eigenvectors characterize a linear transformation and play important roles across the sciences, from geology to quantum mechanics, particularly in feedback systems where the largest eigenvalue governs the system's long-term behavior. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/