Abstract
The Jordan canonical form of the difference of projectors P — Q for the eigenvalues λ ≠ −1, 0, 1 is proved to be made up of pairs of Jordan blocks; i.e., if there are several blocks J k (λ), then there are exactly the same number of blocks J k (−λ). For a block J k (±1) with k > 1, there is necessarily a pair block J l (∓1), where |k — l| < 1.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. N. Anderson, E. Harner, and G. E. Trapp, “Eigenvalues of the difference and product of projections,” Linear Multilinear Algebra 17, 295–299 (1985).
M. Omladic, “Spectra of the difference and product of projections,” Proc. Am. Math. Soc. 99, 317–318 (1987).
M. Baraa and M. Boumazgour, “Spectra of the difference, sum, and product of idempotents,” Studia Math. 148(1), 1–3 (2001).
Kh. D. Ikramov, “Spectral singularities of special classes of matrices,” in Computational Possesses and Systems (Nauka, Moscow, 1991), Vol. 8, pp. 168–203 [in Russian].
Kh. D. Ikramov, Numerical Solution of Matrix Equations (Nauka, Moscow, 1984) [in Russian].
Kh. D. Ikramov, Linear Algebra: Problems Book (Nauka, Moscow, 1975; Mir, Moscow, 1983).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.M. Vetoshkin, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 3, pp. 375–390.
Rights and permissions
About this article
Cite this article
Vetoshkin, A.M. Jordan form of the difference of projectors. Comput. Math. and Math. Phys. 54, 382–396 (2014). https://doi.org/10.1134/S0965542514030178
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542514030178