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Eigenvalues and eigenvectors

Created over 8 years ago, updated 10 days ago

Eigenvalues and eigenvectors capture the intrinsic stretching/compressing directions of a linear transformation. For a square matrix $A$, a nonzero vector $v$ is an eigenvector with eigenvalue $\lambda$ if $Av = \lambda v$. Eigenvalues reveal fundamental properties: invertibility, stability, diagonalizability, and more.