Jordan form of the difference of projectors

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 neces...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2014-03, Vol.54 (3), p.382-396
Main Author: Vetoshkin, A. M.
Format: Article
Language:English
Subjects:
Canonical forms
Computation
Computational mathematics
Computational Mathematics and Numerical Analysis
Eigenvalues
Jordan form
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Physics
Projectors
Studies
Topological manifolds
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542514030178