Eigenvalues And Eigenvectors -

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

): 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

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 ( ): A non-zero vector that, when multiplied by

, does not change its direction; it is only scaled by a scalar factor. Eigenvalue ( ): A non-zero vector that