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JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2025 Number 5, Pages 3–8 (Mi vmumm4712)

Mathematics

Simplified method for calculation of exponent and logarithm of two-dimensional matrix

I. N. Sergeev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A simple algorithm for finding the exponent and real logarithm of a real square matrix of the second order is presented, in which it is not required to reduce it to Jordan form. The method of such calculation of the exponent of a given matrix, proposed by A. F. Filippov, also applies to its logarithms, the set of which may be empty, single-element and infinite — countable and even continuous.

Key words: differential system, linear system, autonomous system, periodic system, Cauchy matrix, matrix exponent, matrix logarithm.

UDC: 517.926

Received: 02.02.2024

DOI: 10.55959/MSU0579-9368-1-66-5-1


 English version:
Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2025, 80:5, 271–277


© Steklov Math. Inst. of RAS, 2026