Email this article On the Symplectic Eigenvalues of Positive Definite Matrices
- Authors: Ikramov K.D.1
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Affiliations:
- Faculty of Computational Mathematics and Cybernetics
- Issue: Vol 42, No 1 (2018)
- Pages: 1-4
- Section: Article
- URL: https://journals.rcsi.science/0278-6419/article/view/176211
- DOI: https://doi.org/10.3103/S0278641918010041
- ID: 176211
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Abstract
A simple proof of Williamson’s theorem is given. This theorem states that a real symmetric positive definite matrix A of even order can be brought to diagonal form Λ by a symplectic congruence transformation. The diagonal entries of Λ are called symplectic eigenvalues of A. The problem of calculating these values is also discussed.
About the authors
Kh. D. Ikramov
Faculty of Computational Mathematics and Cybernetics
Author for correspondence.
Email: ikramov@cs.msu.su
Russian Federation, Moscow, 119991
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