ﻻ يوجد ملخص باللغة العربية
We consider the problem of classifying oriented cycles of linear mappings $F^pto F^qtodotsto F^rto F^p$ over a field $F$ of complex or real numbers up to homeomorphisms in the spaces $F^p,F^q,dots,F^r$. We reduce it to the problem of classifying linear operators $F^nto F^n$ up to homeomorphism in $F^n$, which was studied by N.H. Kuiper and J.W. Robbin [Invent. Math. 19 (2) (1973) 83-106] and by other authors.
We give a method for constructing a regularizing decomposition of a matrix pencil, which is formulated in terms of the linear mappings. We prove that two pencils are topologically equivalent if and only if their regularizing decompositions coincide u
V.I. Arnold [Russian Math. Surveys, 26 (no. 2), 1971, pp. 29-43] gave a miniversal deformation of matrices of linear operators; that is, a simple canonical form, to which not only a given square matrix A, but also the family of all matrices close to
We study systems of linear and semilinear mappings considering them as representations of a directed graph $G$ with full and dashed arrows: a representation of $G$ is given by assigning to each vertex a complex vector space, to each full arrow a line
Two sesquilinear forms $Phi:mathbb C^mtimesmathbb C^mto mathbb C$ and $Psi:mathbb C^ntimesmathbb C^nto mathbb C$ are called topologically equivalent if there exists a homeomorphism $varphi :mathbb C^mto mathbb C^n$ (i.e., a continuous bijection whose
Let $A$ be the locally unital algebra associated to a cyclotomic oriented Brauer category over an arbitrary algebraically closed field $Bbbk$ of characteristic $pge 0$. The category of locally finite dimensional representations of $A $ is used to giv