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Invariant subspaces of matrix algebras and MAPLE procedures detecting their existence

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References

  1. McCoy, N.H., On the Characteristic Roots of Matrix Polynomials,Bull. Amer. Math. Soc., 1936, vol. 42, pp. 592–600.

    MATH  Google Scholar 

  2. Laffey, T.J., Simultaneous Triangularization of Matrices—Low Rank Cases and the Nonderogatory Case,Linear and Multilinear Algebra, 1978, vol. 6, pp. 269–305.

    Article  MATH  MathSciNet  Google Scholar 

  3. McCoy, N.H., On Quasi-commutative Matrices,Trans. Amer. Math. Soc., 1934, vol. 36, pp. 327–340.

    Article  MATH  MathSciNet  Google Scholar 

  4. Shemesh, D., Common Eigenvectors of Two Matrices,Linear Algebra Appl., 1984, vol. 62, pp. 11–18.

    Article  MATH  MathSciNet  Google Scholar 

  5. 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.

    Google Scholar 

  6. George, A. and Ikramov, Kh.D., Common Invariant Subspaces of Two Matrices,Linear Algebra Appl., 1999, vol. 287, pp. 171–179.

    Article  MATH  MathSciNet  Google Scholar 

  7. Gantmakher, F.R.,Teoriya matriz (Matrix Theory), Moscow: Nauka, 1966.

    Google Scholar 

  8. Barker, G.P., Eifler, L.Q., and Kezlan, T.P., A Non-commutative Spectral Theorem,Linear Algebra Appl., 1978, vol. 20, pp. 95–100.

    Article  MATH  MathSciNet  Google Scholar 

  9. Amitsur, S.A. and Levitzki, J., Minimal Identities for Algebras,Proc. Amer. Math. Soc., 1950, vol. 1, pp. 449–463.

    Article  MATH  MathSciNet  Google Scholar 

  10. Formanek, E., Central Polynomials for Matrix Rings,J. Algebra, 1972, vol. 23, pp. 129–131.

    Article  MATH  MathSciNet  Google Scholar 

  11. 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.

    MathSciNet  Google Scholar 

  12. Levitzki, J., A Theorem on Polynomial Identities,Proc. Amer. Math. Soc., 1950, vol. 1, pp. 334–341.

    Article  MATH  MathSciNet  Google Scholar 

  13. Laffey, T.J., Simultaneous Quasidiagonalization of Complex Matrices,Linear Algebra Appl., 1977, vol. 16, pp. 189–201.

    Article  MATH  MathSciNet  Google Scholar 

  14. Djocović, D.Ž., Unitary Similarity of Projectors,Aequationes Math., 1991, vol. 42, pp. 220–224.

    Article  MathSciNet  Google Scholar 

  15. 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.

    MathSciNet  Google Scholar 

  16. 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.

    MathSciNet  Google Scholar 

  17. 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.

    MathSciNet  Google Scholar 

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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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