1. In linear algebra, a scalar value associated with a square matrix such that there exists a non-zero vector (eigenvector) that, when multiplied by the matrix, yields a scalar multiple of that vector.
Usage: technical; mathematics; plural form of eigenvalue

Examples

• The eigenvalues of a 2×2 matrix can be found by solving the characteristic equation.
• In quantum mechanics, eigenvalues represent the possible measured values of an observable.
• The stability of a dynamical system depends on whether the eigenvalues have negative real parts.
• Principal component analysis relies on computing the eigenvalues of the covariance matrix.
• Engineers use eigenvalues to determine the natural frequencies of vibrating structures.