✦ LIBER ✦

On the Kronecker Problem and related problems of Linear Algebra

✍ Scribed by Alexander G. Zavadskij

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 459 KB
Volume: 425
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.03.011

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✦ Synopsis

We consider some classification problems of Linear Algebra related closely to the classical Kronecker Problem on pairs of linear maps between two finite-dimensional vector spaces. As shown by Djoković and Sergeichuk, the Kronecker's solution is extended to the cases of pairs of semilinear maps and (more generally) pseudolinear bundles respectively. Our objective is to deal with the semilinear case of the Kronecker Problem, especially with its applications. It is given a new short solution both to this case and to its contragredient variant. The biquadratic matrix problem is investigated and reduced in the homogeneous case (in characteristic / = 2) to the semilinear Kronecker Problem. The integer matrix sequence n and -transformation of polynomials are introduced and studied to get a simplified canonical form of indecomposables for the mentioned homogeneous problem. Some applications to the representation theory of posets with additional structures are presented.

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