Glasnik matematički, Vol. 42 No. 2, 2007.
Original scientific paper
https://doi.org/10.3336/gm.42.2.04
On linear subspaces of Mn and their singular sets related to the characteristic map
Marcin Skrzynski
orcid.org/0000-0001-7021-220X
; Institute of Mathematics, Cracow University of Technology, ul. Warszawska 24, 31-155 Krakow, Poland
Abstract
We study linear subspaces L Mn (over an algebraically closed field F of characteristic zero) and their singular sets S(L) defined by S(L) = {A Mn : χ(A + L) is not dense in Fn}, where χ : Mn → Fn is the characteristic map. We give a complete characterization of the subspaces L M2 such that ≠ S(L) ≠ M2. We also provide a complete characterization of the singular sets S(L) in the case of n = 2. Finally, we give a characterization of the n-dimensional subspaces L Mn such that S(L) = by means of their intersections with conjugacy classes.
Keywords
Characteristic polynomial of a matrix; characteristic map; dominant map; linear space of matrices; triangularizable set of matrices; conjugacy class of a matrix
Hrčak ID:
17941
URI
Publication date:
11.12.2007.
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