- symplectic matrix
- мат. симплектическая матрица
Большой англо-русский и русско-английский словарь. 2001.
symplectic matrix
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Symplectic matrix — In mathematics, a symplectic matrix is a 2n times; 2n matrix M (whose entries are typically either real or complex) satisfying the condition:M^T Omega M = Omega,.where MT denotes the transpose of M and Omega; is a fixed nonsingular, skew… … Wikipedia
Symplectic vector space — In mathematics, a symplectic vector space is a vector space V equipped with a nondegenerate, skew symmetric, bilinear form omega; called the symplectic form. Explicitly, a symplectic form is a bilinear form omega; : V times; V rarr; R which is *… … Wikipedia
Symplectic manifold — In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2 form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology.… … Wikipedia
Symplectic group — For finite groups with all characteristc abelian subgroups cyclic, see group of symplectic type. Group theory … Wikipedia
Hamiltonian matrix — In mathematics, a Hamiltonian matrix A is any real 2n×2n matrix that satisfies the condition that KA is symmetric, where K is the skew symmetric matrix:K=egin{bmatrix}0 I n I n 0 end{bmatrix}and In is the n×n identity matrix. In other words, A… … Wikipedia
Orthogonal matrix — In linear algebra, an orthogonal matrix (less commonly called orthonormal matrix[1]), is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors). Equivalently, a matrix Q is orthogonal if… … Wikipedia
Skew-symmetric matrix — In linear algebra, a skew symmetric (or antisymmetric) matrix is a square matrix A whose transpose is also its negative; that is, it satisfies the equation:: A T = − A or in component form, if A = ( a ij ):: a ij = − a ji for all i and j .For… … Wikipedia
Unitary matrix — In mathematics, a unitary matrix is an n by n complex matrix U satisfying the condition:U^* U = UU^* = I n, where I n, is the identity matrix and U^* , is the conjugate transpose (also called the Hermitian adjoint) of U . Note this condition says … Wikipedia
Random matrix — In probability theory and mathematical physics, a random matrix is a matrix valued random variable. Many important properties of physical systems can be represented mathematically as matrix problems. For example, the thermal conductivity of a… … Wikipedia
Skew-Hamiltonian matrix — In linear algebra, skew Hamiltonian matrices are special matrices which correspond to skew symmetric bilinear forms on a symplectic vector space.Let V be a vector space, equipped with a symplectic form Omega. Such a space must be even dimensional … Wikipedia
Unimodular matrix — In mathematics, a unimodular matrix M is a square integer matrix with determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix N which is its inverse (these are equivalent under… … Wikipedia
