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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 icon orcid.org/0000-0001-7021-220X ; Institute of Mathematics, Cracow University of Technology, ul. Warszawska 24, 31-155 Krakow, Poland

Puni tekst: engleski, pdf (128 KB) str. 291-299 preuzimanja: 350* citiraj
APA 6th Edition
Skrzynski, M. (2007). On linear subspaces of Mn and their singular sets related to the characteristic map. Glasnik matematički, 42 (2), 291-299. https://doi.org/10.3336/gm.42.2.04
MLA 8th Edition
Skrzynski, Marcin. "On linear subspaces of Mn and their singular sets related to the characteristic map." Glasnik matematički, vol. 42, br. 2, 2007, str. 291-299. https://doi.org/10.3336/gm.42.2.04. Citirano 22.10.2021.
Chicago 17th Edition
Skrzynski, Marcin. "On linear subspaces of Mn and their singular sets related to the characteristic map." Glasnik matematički 42, br. 2 (2007): 291-299. https://doi.org/10.3336/gm.42.2.04
Harvard
Skrzynski, M. (2007). 'On linear subspaces of Mn and their singular sets related to the characteristic map', Glasnik matematički, 42(2), str. 291-299. https://doi.org/10.3336/gm.42.2.04
Vancouver
Skrzynski M. On linear subspaces of Mn and their singular sets related to the characteristic map. Glasnik matematički [Internet]. 2007 [pristupljeno 22.10.2021.];42(2):291-299. https://doi.org/10.3336/gm.42.2.04
IEEE
M. Skrzynski, "On linear subspaces of Mn and their singular sets related to the characteristic map", Glasnik matematički, vol.42, br. 2, str. 291-299, 2007. [Online]. https://doi.org/10.3336/gm.42.2.04

Sažetak
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.

Ključne riječi
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
https://hrcak.srce.hr/17941

Posjeta: 616 *