Variational principles for symplectic eigenvalues
Keyword(s):
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 $d_{i+j-1}(A+B)\geqslant d_i(A)+d_j(B).$
2019 ◽
Vol 21
(07)
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pp. 1850057
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1998 ◽
Vol 26
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pp. 483-496
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1998 ◽
Vol 280
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pp. 199-216
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2014 ◽
Vol 29
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2010 ◽
Vol 62
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pp. 129-142