eigenvalue

noun1

1. •
   A scalar λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear transformation A is equal to the image of x under multiplication by λ; i.e. Ax=λx.

   • To find all the eigenvalues of A, solve the characteristic equation. ¶ For each eigenvalue λ, to find the corresponding set of eigenvectors, solve the linear system of equations […] — 2025