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Glasnik matematički, Vol.42 No.2 December 2007. -

We study linear subspaces L Mn over an algebraically closed field F of characteristic zero and their singular sets SL defined by SL = {A Mn : χA + 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 ≠ SL ≠ M2. We also provide a complete characterization of the singular sets SL in the case of n = 2. Finally, we give a characterization of the n-dimensional subspaces L Mn such that SL = by means of their intersections with conjugacy classes.

Characteristic polynomial of a matrix; characteristic map; dominant map; linear space of matrices; triangularizable set of matrices; conjugacy class of a matrix



Author: Marcin Skrzynski - orcid.org-0000-0001-7021-220X ; Institute of Mathematics, Cracow University of Technology, ul. Warszawska 24,

Source: http://hrcak.srce.hr/



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