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Variational principles for symplectic eigenvalues
- Source :
- Canadian Mathematical Bulletin. 64:553-559
- Publication Year :
- 2020
- Publisher :
- Canadian Mathematical Society, 2020.
-
Abstract
- If A is a real $2n \times 2n$ positive definite matrix, then there exists a symplectic matrix M such that $M^TAM=\text {diag}(D, D),$ where D is a positive diagonal matrix with diagonal entries $d_1(A)\leqslant \cdots \leqslant d_n(A).$ We prove a maxmin principle for $d_k(A)$ akin to the classical Courant–Fisher–Weyl principle for Hermitian eigenvalues and use it to derive an analogue of the Weyl inequality $d_{i+j-1}(A+B)\geqslant d_i(A)+d_j(B).$
Details
- ISSN :
- 14964287 and 00084395
- Volume :
- 64
- Database :
- OpenAIRE
- Journal :
- Canadian Mathematical Bulletin
- Accession number :
- edsair.doi...........dfa2cbcf44b8742ae896797981411f44