Word.ws English Dictionary

symplectic matrix

symplectic matrix 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).

Noun

symplectic matrix (plural symplectic matrices)

  1. 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).
    • 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.2001, Alberto Abbondandolo, Morse Theory for Hamiltonian Systems, CRC Press (Chapman & Hall/CRC), page x
    • 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...2002, Heike Fassbender, Symplectic Methods for the Symplectic Eigenproblem, Kluwer Academic, page 173

Forms of symplectic matrix

pluralsymplectic matrices

Questions about symplectic matrix

What does symplectic matrix mean?
Symplectic matrix means 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).
What part of speech is symplectic matrix?
Symplectic matrix is a noun.
What is the plural of symplectic matrix?
The plural of symplectic matrix is symplectic matrices.

Words near symplectic matrix in the dictionary

  1. symplasts
  2. symplectic
  3. symplectic group
  4. symplectic groups
  5. symplectic matrices
  6. symplectic matrix
  7. symplectically
  8. symplecticity
  9. symplectics
  10. symplectisation
  11. symplectisations

Source and license

Adapted from Wiktionary: symplectic matrix (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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