On Some “Tame” and “Wild” Aspects of the Problem of Semiscalar Equivalence of Polynomial Matrices

被引：0
作者：
B. Z. Shavarovskii
机构：
[1] Ya. S. Pidstrigach Institute of Applied Problems of Mechanics and Mathematics,National Academy of Sciences of Ukraine
来源：
Mathematical Notes | 2004年 / 76卷
关键词：
polynomial matrix; semiscalar equivalence; tame problem; wild problem;
D O I：
暂无
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学科分类号：
摘要：
The problem of reducing polynomial matrices to canonical form by using semiscalar equivalent transformations is studied. This problem is wild as a whole. However, it is tame in some special cases. In the paper, classes of polynomial matrices are singled out for which canonical forms with respect to semiscalar equivalence are indicated. We use this tool to construct a canonical form for the families of coefficients corresponding to the polynomial matrices. This form enables one to solve the classification problem for families of numerical matrices up to similarity.
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页码：111 / 123
页数：12
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共 14 条
  • [1] Donovan P.(1973)"Some evidence for an extension of the Brauer-Thrall conjecture," Sonderforschungsbereich Theor. Math. 40 24-26
  • [2] Freislich M. R.(1968)Indecomposable representations of the Lorentz group Uspekhi Mat. Nauk 23 3-60
  • [3] Gel′fand I. M.(1973)A certain problem of I. M. Gelfand Funktsional. Anal. i Prilozhen 7 54-69
  • [4] Ponomarev V. A.(1975)Representations of dihedral groups over a field of characteristic 2 Mat. Sb. 96 63-74
  • [5] Nazarova L. A.(1977)The representation type of finite groups Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 71 24-42
  • [6] Roiter A. V.(1983)Simultaneous similarity of matrices Adv. Math. 50 189-265
  • [7] Bondarenko V. M.(2000)Normal forms in matrix spaces Integral Equations Operator Theory 30 251-283
  • [8] Bondarenko V. M.(2000)Canonical matrices for linear matrix problems Linear Algebra Appl. 317 53-102
  • [9] Drozd Y. A.(2000)On a criterion for the diagonalizability of real matrices Zh. Vychisl. Mat. Mat. Fiz. [Comput. Math. Math. Phys.] 40 6-20
  • [10] Friedland S.(1998)Reduction of matrices by means of equivalent and similar transformations Mat. Zametki 64 769-782
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