Eigenvalues And Eigenvectors -

The concepts of and eigenvectors are fundamental in linear algebra for understanding how a linear transformation (represented by a matrix ) scales space along certain directions. Core Definitions Eigenvector (

): The scalar factor by which the eigenvector is stretched or compressed. These are related by the equation , which can be rewritten to find eigenvalues as is the identity matrix. Key Feature Applications Eigenvalues and Eigenvectors

Eigenvalues and eigenvectors are "features" themselves in many computational and analytical processes: The concepts of and eigenvectors are fundamental in

): A non-zero vector that, when multiplied by a square matrix when multiplied by a square matrix

, does not change its direction; it is only scaled by a scalar factor. Eigenvalue (