Minimal indices and minimal bases via filtrations

Mackey, D. Steven (2012) Minimal indices and minimal bases via filtrations. [MIMS Preprint]

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Abstract

In this note we develop a new way of formulating the notions of minimal basis and minimal indices, based on the concept of a filtration of a vector space. The goal is to provide useful new tools for working with these important concepts, as well as to gain deeper insight into their fundamental nature. This approach also readily reveals a strong minimality property of minimal indices, from which follows a characterization of the vector polynomial bases in rational vector spaces. The effectiveness of this new formulation is further illustrated by proving two fundamental properties: the invariance of the minimal indices of a matrix polynomial under field extension, and the direct sum property of minimal indices.

Item Type: MIMS Preprint
Uncontrolled Keywords: singular matrix polynomial, minimal indices, minimal basis, filtration, flag
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr. D. Steven Mackey
Date Deposited: 29 Jan 2014
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2093

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