Meaning of symplectic matrix | Babel Free

Definitions

For given field F (especially the real numbers), even order 2n and nonsingular skew-symmetric matrix Ω, any 2n×2n matrix M with elements in F such that MᵀΩM = Ω (where Mᵀ denotes the transpose of M).

Equivalents

Examples

“Then we define⟳ the Krein signature of the eigenvalues of modulus one of a symplectic matrix and use⟳ this concept to build⟳ the rotation function on the symplectic group.”

“In the previous chapter algorithms for computing the eigenvalues of symplectic matrices have⟳ been considered that are based on an elimination process⟳ for computing the butterfly form⟳ of symplectic matrix. Unfortunately, this approach⟳ is not suitable when dealing with large and sparse symplectic matrices as an elimination process⟳ can not make⟳ full use⟳ of the sparsity.”

“In order⟳ to fully exploit these structures we rely⟳ on the properties of Hamiltonian, skew-Hamiltonian, and symplectic matrices discussed in Section 1.5. In Section 4.1 we introduce⟳ the elementary symplectic matrices which are used by the structured algorithms.”

CEFR level