Abstract
Using methods of the representation theory of finite-dimensional associative algebras, the paper presents an explicit classification of the pairs of real subspaces of a finite-dimensional complex vector space in terms of complex matrices. Thus, we classify the orbits of the direct product GL(m, C) × GL(m 1, R) × GL(m 2, R) acting on the set of pairs of m × m t complex matrices A t , t = 1,2, by (A 1,A 2)(Q,P 1,P 2) = (QA 1P −1 1,QA 2P −1 2). In addition, the general case of canonical forms of pairs of complex matrices is resolved.
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