symplectic matrix
Word Rarity
Very rare
Frequency: Zipf frequency 2.00 in modern English
36
Scrabble Score
16
Letters
5
Syllables
12
Unique Chars
Meaning
noun
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).
Example Sentences
- "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."