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An eigenvalue (λ) is a scalar with a particular relationship to some particular matrix. An eigenvector of a matrix is a non-zero vector, which when multiplied by the (necessarily square) matrix (performing a linear transformation on the vector), produces a vector that is the same as that eigenvector multiplied by a scalar constant, the constant termed an eigenvalue of the matrix. A matrix may have more than one eigenvector and eigenvalue. Eigen-decomposition is the determination of an eigenvector and associated eigenvalue of a matrix. Eigenvalues and eigenvectors have applications in geometric transformations, in quantum mechanics, and in other physical phenomena.