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Property of polynomials in two projectors

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Abstract

It is proved that a polynomial in two projectors vanishes for all pairs of projectors only if all the coefficients of this polynomial are equal to zero.

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References

  1. A. G. Kurosh, A Course in Higher Algebra (Nauka, Moscow, 1968; Mir, Moscow, 1975).

    Google Scholar 

  2. V. V. Prasolov, Problems and Theorems in Linear Algebra (Am. Math. Soc., Providence, 1994; Fizmatlit, Moscow, 1996).

    MATH  Google Scholar 

  3. Kh. D. Ikramov, “Simultaneous reduction to block triangular form and theorems on pairs of complex idempotents,” Comput. Math. Math. Phys. 51(6), 915–918 (2011).

    Article  MathSciNet  Google Scholar 

  4. Kh. D. Ikramov, “On simultaneous reduction of a pair of oblique projectors to block triangular form,” Comput. Math. Math. Phys. 38(2), 173–174 (1998).

    MathSciNet  Google Scholar 

  5. A. George and Kh. D. Ikramov, “A note on the canonical form for a pair of orthoprojectors,” J. Math. Sci. 132(2), 153–155 (2006).

    Article  MathSciNet  Google Scholar 

  6. Kh. D. Ikramov, “The canonical forms of projectors with respect to unitary similarity and their applications,” Comput. Math. Math. Phys. 44(9), 1456–1461 (2004).

    MathSciNet  Google Scholar 

  7. A. M. Vetoshkin, “Matrix polynomials in variable projectors that are projectors themselves,” in Automation and Computerization of Data Processing Techniques and Technologies (Mosk. Gos. Univ. Lesa, Moscow, 2008), Vol. 341, pp. 69–78 [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Electronics and Systems Engineering, Moscow State Forest University, Pervaya Institutskaya ul., 1, Mytishchi-5, Moscow oblast, 141005, Russia

    A. M. Vetoshkin

Authors
  1. A. M. Vetoshkin
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Correspondence to A. M. Vetoshkin.

Additional information

Original Russian Text © A.M. Vetoshkin, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 2, pp. 189–192.

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Vetoshkin, A.M. Property of polynomials in two projectors. Comput. Math. and Math. Phys. 55, 179–182 (2015). https://doi.org/10.1134/S0965542515020190

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  • DOI: https://doi.org/10.1134/S0965542515020190

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