ON THE BOUNDS OF EIGENVALUES
Kyuichiro WASHIZU · The Quarterly Journal of Mechanics and Applied Mathematics · 1955
In this paper, formulae for locating the bounds of eigenvalues of a real symmetric matrix are treated in a unified manner. In the first part of the paper, several theorems which provide bounds for eigenvalues are represented in a geometrical space. In the second part, a generalization of Rayleigh's principle is attempted, and some theorems which provide bounds for eigenvalues are discussed as special cases of the generalized Rayleigh's principle. The system treated here has a finite number of degrees of freedom. By appropriate modifications the above principles can, however, be extended to a system with an infinite number of degrees of freedom.