Abstract
In the present paper the problem of classifying blocks of matrices up to similarity is considered. The notion of block similarity used here is a natural generalization of similarity for matrices. The invariants are described and canonical forms are given. This theory of block-similarity provides a general framework, which includes the state feedback theory for systems, the theory of Kronecker equivalence and a similarity theory for non-everywhere defined operators. New applications, in particular to factorization problems, are also obtained.
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Gohberg, I., Kaashoek, M.A. & van Schagen, F. Similarity of operator blocks and canonical forms. I. General results, feedback equivalence and kronecker indices. Integr equ oper theory 3, 350–396 (1980). https://doi.org/10.1007/BF01701498
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DOI: https://doi.org/10.1007/BF01701498