Premium
On Families of Square Matrices
Author(s) -
Bruce J. W.,
Tari F.
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504014911
Subject(s) - mathematics , invertible matrix , mathematics subject classification , square (algebra) , moduli space , equivalence (formal languages) , manifold (fluid mechanics) , pure mathematics , square matrix , simple (philosophy) , space (punctuation) , algebra over a field , combinatorics , eigenvalues and eigenvectors , geometry , symmetric matrix , mechanical engineering , philosophy , physics , linguistics , epistemology , quantum mechanics , engineering
In this paper we classify families of square matrices up to the following natural equivalence. Thinking of these families as germs of smooth mappings from a manifold to the space of square matrices, we allow arbitrary smooth changes of co‐ordinates in the source and pre‐ and post‐ multiply our family of matrices by (generally distinct) families of invertible matrices, all dependent on the same variables. We obtain a list of all the corresponding simple mappings (that is, those that do not involve adjacent moduli). This is a non‐linear generalisation of the classical notion of linear systems of matrices. We also make a start on an understanding of the associated geometry. 2000 Mathematics Subject Classification 58K40, 58K50, 58K60, 32S25.