Minimal subadditive inclusion domains for the eigenvalues of matrices

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Abstract

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.

Original languageEnglish
Pages (from-to)233-268
Number of pages36
JournalLinear Algebra and Its Applications
Volume17
Issue number3
DOIs
StatePublished - 1977
Externally publishedYes

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