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Unitary similarity of algebras generated by pairs of orthoprojectors

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Abstract

It is shown that the unitary similarity of two matrix algebras generated by pairs of orthoprojectors { P1, Q1} and {P2,Q2} can be verified by comparing the traces of P1, Q1, and (P1Q1)i, i = 1, 2, …, n, with those of P2, Q2, and (P2Q2)i. The conditions of the unitary similarity of two matrices with quadratic minimal polynomials presented in [A. George and Kh. D. Ikramov, Unitary similarity of matrices with quadratic minimal polynomials, Linear Algebra Appl., 349, 11–16 (2002)] are refined. Bibliography: 10 titles.

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Authors and Affiliations

  1. Kazan’ State University, Kazan’, Russia

    Yu. A. Al’pin

  2. Moscow State University, Moscow, Russia

    Kh. D. Ikramov

Authors
  1. Yu. A. Al’pin
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  2. Kh. D. Ikramov
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 5–14.

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Al’pin, Y.A., Ikramov, K.D. Unitary similarity of algebras generated by pairs of orthoprojectors. J Math Sci 137, 4763–4768 (2006). https://doi.org/10.1007/s10958-006-0272-x

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  • DOI: https://doi.org/10.1007/s10958-006-0272-x

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