On the shifted eigenvalue problem
- 1 January 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 67 (1) , 97-99
- https://doi.org/10.1017/s0305004100057145
Abstract
Lanczos(1, 2) has considered the shifted eigenvalue problem where C is a (p × q) matrix of rank r, CH is its hermitean conjugate and u, v are column vectors of orders p, q respectively. In this note we extend Lanczos' work to cover the more general eigenvalue problem which arises in certain problems in solid state physics (3). In (2), the I's are unit matrices of appropriate orders and the constants a, b are real; the partitioned matrix M is thus hermitean so that its eigenvalues λ are real.This publication has 1 reference indexed in Scilit:
- Linear Systems in Self-Adjoint FormThe American Mathematical Monthly, 1958