Geodesic
Similarity transformations of decomposable matrix polynomials and related questions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1539-1553

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A elationship is found between the similarity transformations of decomposable matrix polynomials with relatively prime elementary divisors and the equivalence transformations of the corresponding matrices with scalar entries. Matrices with scalar entries are classified with respect to equivalence transformations based on direct sums of lower triangular almost Toeplitz matrices. This solves the similarity problem for a special class of finite matrix sets over the field of complex numbers. Eventually, this problem reduces to the one of special diagonal equivalence between matrices. Invariants of this equivalence are found. 
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     author = {B. Z. Shavarovskii},
     title = {Similarity transformations of decomposable matrix polynomials and related questions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1539--1553},
     publisher = {mathdoc},
     volume = {49},
     number = {9},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a0/}
}
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B. Z. Shavarovskii. Similarity transformations of decomposable matrix polynomials and related questions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1539-1553. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a0/