DefinitionEigenvalue methods are a class of mathematical techniques for solving systems of linear equations, based on eigenvalues and eigenvectors of matrices. Diagonalization, Power iteration, QR algorithm, Singular value decomposition (SVD), Iterative methods – Jacobi and Gauss-Seidel iterations. Eigenvalue methods are a classical tool in linear algebra, numerical analysis, quantum mechanics, and control theory for studying dynamical systems, natural modes of vibration, and optimization problems. It offers some impressive robust algorithms for scaling systems of equations and eigenvalue problems. Similarly the power iteration method calculates the biggest eigenvalue and its out of the list is equivalently associated eigenvector of a matrix by repetitive multiplication of the matrix to an arbitrary initial vector each time normalizing the result.
