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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 (
, does not change its direction; it is only scaled by a scalar factor. Eigenvalue ( Eigenvalues and Eigenvectors
): A non-zero vector that, when multiplied by a square matrix The concepts of and eigenvectors are fundamental in
): 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 does not change its direction
Eigenvalues and eigenvectors are "features" themselves in many computational and analytical processes: