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A remark on spaces over a special local ring

Marek Jukl (1998)

Mathematica Bohemica

This paper deals with A-spaces in the sense of McDonald over linear algebras A of a certain type. Necessary and sufficient conditions for a submodule to be an A-space are derived.

A result related to the largest eigenvalue of a tree

Gurusamy Rengasamy Vijayakumar (2008)

Discussiones Mathematicae Graph Theory

In this note we prove that {0,1,√2,√3,2} is the set of all real numbers l such that the following holds: every tree having an eigenvalue which is larger than l has a subtree whose largest eigenvalue is l.

A review of selected topics in majorization theory

Marek Niezgoda (2013)

Banach Center Publications

In this expository paper, some recent developments in majorization theory are reviewed. Selected topics on group majorizations, group-induced cone orderings, Eaton triples, normal decomposition systems and similarly separable vectors are discussed. Special attention is devoted to majorization inequalities. A unified approach is presented for proving majorization relations for eigenvalues and singular values of matrices. Some methods based on the Chebyshev functional and similarly separable vectors...

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