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- Symplectic_matrix abstract "In mathematics, a symplectic matrix is a 2n×2n matrix M with real entries that satisfies the condition</dl>where MT denotes the transpose of M and Ω is a fixed 2n×2n nonsingular, skew-symmetric matrix. This definition can be extended to 2n×2n matrices with entries in other fields, e.g. the complex numbers.Typically Ω is chosen to be the block matrixwhere In is the n×n identity matrix. The matrix Ω has determinant +1 and has an inverse given by Ω−1 = ΩT = −Ω.Every symplectic matrix has unit determinant, and the 2n×2n symplectic matrices with real entries form a subgroup of the special linear group SL(2n, R) under matrix multiplication, specifically a connected noncompact real Lie group of real dimension n(2n + 1), the symplectic group Sp(2n, R). The symplectic group can be defined as the set of linear transformations that preserve the symplectic form of a real symplectic vector space.".
- Symplectic_matrix wikiPageID "173983".
- Symplectic_matrix wikiPageRevisionID "571486516".
- Symplectic_matrix hasPhotoCollection Symplectic_matrix.
- Symplectic_matrix id "4140".
- Symplectic_matrix id "7455".
- Symplectic_matrix title "Symplectic matrix".
- Symplectic_matrix title "The characteristic polynomial of a symplectic matrix is a reciprocal polynomial".
- Symplectic_matrix subject Category:Matrices.
- Symplectic_matrix subject Category:Symplectic_geometry.
- Symplectic_matrix type Abstraction100002137.
- Symplectic_matrix type Arrangement107938773.
- Symplectic_matrix type Array107939382.
- Symplectic_matrix type Group100031264.
- Symplectic_matrix type Matrices.
- Symplectic_matrix type Matrix108267640.
- Symplectic_matrix comment "In mathematics, a symplectic matrix is a 2n×2n matrix M with real entries that satisfies the condition</dl>where MT denotes the transpose of M and Ω is a fixed 2n×2n nonsingular, skew-symmetric matrix. This definition can be extended to 2n×2n matrices with entries in other fields, e.g. the complex numbers.Typically Ω is chosen to be the block matrixwhere In is the n×n identity matrix.".
- Symplectic_matrix label "Matrice simplettica".
- Symplectic_matrix label "Matrice symplectique".
- Symplectic_matrix label "Symplectic matrix".
- Symplectic_matrix label "Symplectische matrix".
- Symplectic_matrix label "斜交行列".
- Symplectic_matrix label "辛矩陣".
- Symplectic_matrix sameAs Matrice_symplectique.
- Symplectic_matrix sameAs Matrice_simplettica.
- Symplectic_matrix sameAs 斜交行列.
- Symplectic_matrix sameAs 심플렉틱_행렬.
- Symplectic_matrix sameAs Symplectische_matrix.
- Symplectic_matrix sameAs m.017gtm.
- Symplectic_matrix sameAs Q2705070.
- Symplectic_matrix sameAs Q2705070.
- Symplectic_matrix sameAs Symplectic_matrix.
- Symplectic_matrix wasDerivedFrom Symplectic_matrix?oldid=571486516.
- Symplectic_matrix isPrimaryTopicOf Symplectic_matrix.