nonsingular transformation
1similarity transformation — Math. 1. Also called homothetic transformation. a mapping of a set by which each element in the set is mapped into a positive constant multiple of itself, the same constant being used for all elements. 2. an operation performed upon a square… …
2similarity transformation — Math. 1. Also called homothetic transformation. a mapping of a set by which each element in the set is mapped into a positive constant multiple of itself, the same constant being used for all elements. 2. an operation performed upon a square… …
3Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… …
4Symplectic 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… …
5Invertible matrix — In linear algebra an n by n (square) matrix A is called invertible (some authors use nonsingular or nondegenerate) if there exists an n by n matrix B such that where In denotes the n by n identity matrix and the multiplication used is ordinary… …
6Symplectic 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 *… …
7Generalized flag variety — In mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth …
8Collineation — In projective geometry, a collineation is a one to one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear. All projective linear …
9CCR and CAR algebras — In quantum field theory, if V is a real vector space equipped with a nonsingular real antisymmetric bilinear form (,) (i.e. a symplectic vector space), the unital * algebra generated by elements of V subject to the relations :fg gf=i(f,g):f*=ffor …
10matrix — /may triks, ma /, n., pl. matrices /may tri seez , ma /, matrixes. 1. something that constitutes the place or point from which something else originates, takes form, or develops: The Greco Roman world was the matrix for Western civilization. 2.… …
