We consider the two parameter eigenvalue problem Tjvj - λ1Aj1vj - λ2Aj2vj = 0, where λj C; Tj, Ajk (j,k=1,2) are matrices. Bounds for the spectral radius of that problem are suggested. Our main tool is a norm estimate for the operator inverse to the operator A11 ⊗ A22 - A12 ⊗ A21, where ⊗ means the tensor product. In addition, by virtue of that norm estimate and the Ostrowsky-Schneider theorem we establish a condition that provides the conservation of the number of the eigenvalues of the considered problem in a half-plane.
- Ostrowsky-Schneider theorem
- Two parameter matrix eigenvalue problem
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics