3. The Symmetric Eigenvalue Problem
George Walter Stewart · Society for Industrial and Applied Mathematics eBooks · 2001
We have seen that symmetric (or Hermitian) matrices have special mathematical properties. In particular, their eigenvalues are real and their eigenvectors can be chosen to form an orthonormal basis for ℝn. They also have special computational properties. Because of their symmetry they can be stored in about half the memory required for a general matrix. Moreover, we can frequently use the symmetry of the problem to reduce the operation count in certain algorithms. For example, the Cholesky algorithm for triangularizing a symmetric matrix requires half the operations that are required by its nonsymmetric counterpart, Gaussian elimination (see Algorithm I:2.2.1).