Poset block equivalence of integral matrices

Authors:
Mike Boyle and Danrun Huang

Journal:
Trans. Amer. Math. Soc. **355** (2003), 3861-3886

MSC (2000):
Primary 15A21; Secondary 06A11, 06F99, 15A36, 16G20, 37B10, 46L35

DOI:
https://doi.org/10.1090/S0002-9947-03-02947-7

Published electronically:
June 10, 2003

MathSciNet review:
1990568

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Given square matrices and with a poset-indexed block structure (for which an block is zero unless ), when are there invertible matrices and with this required-zero-block structure such that ? We give complete invariants for the existence of such an equivalence for matrices over a principal ideal domain . As one application, when is a field we classify such matrices up to similarity by matrices respecting the block structure. We also give complete invariants for equivalence under the additional requirement that the diagonal blocks of and have determinant . The invariants involve an associated diagram (the ``-web'') of -module homomorphisms. The study is motivated by applications to symbolic dynamics and -algebras.

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Additional Information

**Mike Boyle**

Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015

Email:
mmb@math.umd.edu

**Danrun Huang**

Affiliation:
Department of Mathematics, St. Cloud State University, St. Cloud, Minnesota 56301-4498

Email:
dhuang@stcloudstate.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-02947-7

Keywords:
Block,
equivalence,
poset,
integer,
matrix,
principal ideal domain,
cokernel,
flow equivalence,
representation,
similarity

Received by editor(s):
September 13, 2000

Published electronically:
June 10, 2003

Additional Notes:
The first author gratefully acknowledges support of NSF Grant DMS9706852, and sabbatical support from the University of Maryland and the University of Washington. The second author gratefully acknowledges support of Research Grant 211243 from the St. Cloud State University

Article copyright:
© Copyright 2003
American Mathematical Society