[01] Yuri N. Bazilevich, Department of Applied Mathematics, Prydniprovsk State Academy of Civil Engineering and Architecture, Dnipropetrovs'k, Ukraine.

The solution of the problem of several n×n matrices reduction to the same upper block-triangular form by a similarity transformation with the greatest possible number of blocks on the main diagonal is given. In addition to the well-known "method of commutative matrix" a new "method of invariant subspace" is used.

Matrix, Block-Triangular Form, Similarity Transformation, the Centralizer, Algebra over the Field, Radical Ideal

[01] Bazilevich Yu. N., Numerical decoupling methods in the linear problems of mechanics, Kyiv, Naukova Dumka, 1987 (in Russian). [02] Bazilevich Yu. N., Korotenko M.L. and Shvets I.V., Solving the problem on hierarchical decoupling the linear mathematical models of mechanical systems, Tekhnicheskaya Mekhanika, 2003, N 1, 135–141 (in Russian). [03] Bazilevich Yu. N., The exact decoupling of linear systems, Electronic Journal “Issledovano v Rossii”, 2006, 018, 182–190, http://www.sci-journal.ru/articles/2006/018.pdf (in Russian). [04] Drozd Yu. A., Tame and wild matrix problems, Lect. Notes Math., 832, 242-258 (1980). [05] Fermi Enrico, Notes on quantum mechanics/ The University of Chicago Pres [06] Lopatin A.K., The algebraic reducibility of systems of linear differential equations. I, Diff. Uravn., 1968, V.4, 439–445 (in Russian). [07] Yakubovich E.D., Construction of replacement systems for a class of multidimensional linear automatic control systems, Izv. Vuzov, Radiofizika, 1969, V.12, N 3, 362–377 (in Russian). [08] Gantmacher F. R., The Theory of Matrices / Chelsea: New York. 1960. [09] Bazilevich Yu. N., Buldovich A.L., Algorithm for finding the general solution of the system of linear homogeneous algebraic equations in the case of very large-scale sparse matrix coefficients // Mathematical models and modern technology. Coll. scientific. tr. / NAS. Institute of Mathematics. - Kyiv, 1998. — 12, 13 (in Russian). [10] Van Der Waerden Algebra. vols. I and II. Springer-Verlag. [11] Chebotariov N.G., Introduction to theory of algebras, Moscow: Editorial URSS, 2003 (in Russian). [12] Belozerov V.E., Mozhaev G.V., The uniqueness of the solution of problems of decoupling and aggregation of linear systems of automatic control // Teoriya slozhnyih sistem i metodyi ih modelirovaniya.— M: VNIISI, 1982.— 4-13 (in Russian). [13] Bazilevich Yu. N. Hidden Symmetry Exposure. The Mechanical Systems with the Hard Structure of Forces // Proceedings of Institute of Mathematics of NAS of Ukraine. — V. 50. — Part 3. — Kyiv: Institute of Mathematics of NAS of Ukraine, 2004 /— P. 1261—1265. [14] Pavlovsky Yu. N., Smirnova T.G., The problem of decomposition in the mathematical modeling.— M .: FAZIS, 1998. VI + 266 (in Russian).