Poset Block Equivalence of Integral Matrices
نویسندگان
چکیده
Given square matrices B and B′ with a poset-indexed block structure (for which an ij block is zero unless i j), when are there invertible matrices U and V with this required-zero-block structure such that UBV = B′? We give complete invariants for the existence of such an equivalence for matrices over a principal ideal domain R. As one application, when R 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 U and V have determinant 1. The invariants involve an associated diagram (the “K-web”) of R-module homomorphisms. The study is motivated by applications to symbolic dynamics and C∗-algebras.
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تاریخ انتشار 2000