References
McCoy, N.H., On the Characteristic Roots of Matrix Polynomials,Bull. Amer. Math. Soc., 1936, vol. 42, pp. 592–600.
Laffey, T.J., Simultaneous Triangularization of Matrices—Low Rank Cases and the Nonderogatory Case,Linear and Multilinear Algebra, 1978, vol. 6, pp. 269–305.
McCoy, N.H., On Quasi-commutative Matrices,Trans. Amer. Math. Soc., 1934, vol. 36, pp. 327–340.
Shemesh, D., Common Eigenvectors of Two Matrices,Linear Algebra Appl., 1984, vol. 62, pp. 11–18.
Ikramov, Kh.D., Savel'eva, N.V., and Chugunov, V.N., On Computer Algebra Procedures Detecting the Existence of Common Eigenspaces or Invariant Spaces, inMetody matematicheskogo modelirovaniya (Methods of Mathematical Simulation), Moscow: Izd. Mosk. Univ., 1998, pp. 5–23.
George, A. and Ikramov, Kh.D., Common Invariant Subspaces of Two Matrices,Linear Algebra Appl., 1999, vol. 287, pp. 171–179.
Gantmakher, F.R.,Teoriya matriz (Matrix Theory), Moscow: Nauka, 1966.
Barker, G.P., Eifler, L.Q., and Kezlan, T.P., A Non-commutative Spectral Theorem,Linear Algebra Appl., 1978, vol. 20, pp. 95–100.
Amitsur, S.A. and Levitzki, J., Minimal Identities for Algebras,Proc. Amer. Math. Soc., 1950, vol. 1, pp. 449–463.
Formanek, E., Central Polynomials for Matrix Rings,J. Algebra, 1972, vol. 23, pp. 129–131.
Razmyslov, Yu.P., Trace Identities of Full Matrix Algebras Over a Field of Characteristic Zero,Izv. Akad. Nauk SSSR. Matematika, 1974, vol. 38, no. 4, pp. 723–756.
Levitzki, J., A Theorem on Polynomial Identities,Proc. Amer. Math. Soc., 1950, vol. 1, pp. 334–341.
Laffey, T.J., Simultaneous Quasidiagonalization of Complex Matrices,Linear Algebra Appl., 1977, vol. 16, pp. 189–201.
Djocović, D.Ž., Unitary Similarity of Projectors,Aequationes Math., 1991, vol. 42, pp. 220–224.
Ikramov, Kh.D., The Canonical Schur Form of a Unitarily Quasidiagonalizable Matrix,Zh. Vychisl. Mat. Mat. Fiz., 1997, vol. 37, no. 12, pp. 1411–1415.
Bulatovich, R.M., Simultaneous Reduction of a Symmetric Matrix and a Skew-symmetric One to Canonical Form,Mat. Zrne Gore, 1997, vol. 8, pp. 33–36.
Ikramov, Kh.D. and Savel'eva, N.V., On Certain Quasidiagonalizable Families of Matrices,Zh. Vychisl. Mat. Mat. Fiz., 1998, vol. 38, no. 7, pp. 1075–1084.
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Ikramov, K.D., Savel’eva, N.V. Invariant subspaces of matrix algebras and MAPLE procedures detecting their existence. Program Comput Soft 26, 100–103 (2000). https://doi.org/10.1007/BF02759196
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DOI: https://doi.org/10.1007/BF02759196