Abstract
It is shown that if a block triangular matrix is similar to its block diagonal part, then the similarity matrix can be chosen of the block triangular form. An analogous statement is proved for equivalent matrices. For the simplest case of 2×2 block matrices these results were obtained by W.Roth [1]. It is shown that all these results do not admit a generalization for the infinite dimensional case.
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Olshevsky, V. Similarity of block diagonal and block triangular matrices. Integr equ oper theory 15, 853–863 (1992). https://doi.org/10.1007/BF01200704
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DOI: https://doi.org/10.1007/BF01200704