The inverse eigenvalue problem for Hermitian matrices whose graphs are cycles
- 21 September 2009
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 57 (7) , 673-682
Abstract
In 1979, Ferguson characterized the periodic Jacobi matrices with given eigenvalues and showed how to use the Lanzcos Algorithm to construct each such matrix. This article provides general characterizations and constructions for the complex analogue of periodic Jacobi matrices. As a consequence of the main procedure, we prove that the multiplicity of an eigenvalue of a periodic Jacobi matrix is at most 2.Keywords
This publication has 10 references indexed in Scilit:
- Spectral Estimates for Periodic Jacobi MatricesCommunications in Mathematical Physics, 2003
- Continued fractions and periodic jacobi matricesLinear Algebra and its Applications, 1992
- Matrices, Digraphs, and DeterminantsSIAM Journal on Matrix Analysis and Applications, 1989
- Construction of acyclic matrices from spectral dataLinear Algebra and its Applications, 1989
- A modified method for reconstructing periodic Jacobi matricesMathematics of Computation, 1984
- The construction of Jacobi and periodic Jacobi matrices with prescribed spectraMathematics of Computation, 1980
- The spectrum of Jacobi matricesInventiones Mathematicae, 1976
- Construction of a Jacobi matrix from spectral dataLinear Algebra and its Applications, 1976
- Inverse eigenvalue problems for Jacobi matricesLinear Algebra and its Applications, 1976
- On the construction of a Jacobi matrix from spectral dataLinear Algebra and its Applications, 1974