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Minimal subadditive inclusion domains for the eigenvalues of matrices

1977; Elsevier BV; Volume: 17; Issue: 3 Linguagem: Inglês

10.1016/0024-3795(77)90063-5

1873-1856

Christoph Zenger,

Advanced Topics in Algebra

Minimal subadditive inclusion sets for the eigenvalues of matrices are constructed as numerical ranges based on a relation called parallelism which generalizes Bauer's dual vector pairs and Lumers semi-inner-product spaces. The corresponding sets of dissipative matrices are shown to be maximal convex cones of nonsingular matrices. The results are useful as a basis for an axiomatic definition of numerical ranges not restricted to normed algebras. The invariance of certain cones of dissipative matrices under the mapping of a matrix to its negative quasiinverse is stated, and some applications of this result are given.