The portion of matrices with real spectrum in the real orthogonal Lie algebra

A. S. Krivonogov^a, V. A. Churkin<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: The portion of matrices with real spectrum in a matrix Lie algebra is the ratio of the volume of the set of matrices with real spectrum in a ball centered at the zero of the algebra to the volume of the whole ball. We calculate the portion for the real orthogonal Lie algebra.

Keywords: real orthogonal Lie algebra, random matrices with real spectrum.

UDC: 512.643

Received: 15.03.2015

DOI: 10.17377/smzh.2016.57.213

 English version: Siberian Mathematical Journal, 2016, 57:2, 303–321

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