nondegenerate
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nondegenerate — adj., n.; nondegenerately, adv.; nondegenerateness, n. * * * … Universalium
nondegenerate — adj., n.; nondegenerately, adv.; nondegenerateness, n … Useful english dictionary
Bilinear form — In mathematics, a bilinear form on a vector space V is a bilinear mapping V × V → F , where F is the field of scalars. That is, a bilinear form is a function B : V × V → F which is linear in each argument separately::egin{array}{l} ext{1. }B(u + … Wikipedia
Degenerate form — For other uses, see Degeneracy. In mathematics, specifically linear algebra, a degenerate bilinear form ƒ(x,y) on a vector space V is one such that the map from V to V * (the dual space of V) given by is not an isomorphism. An equivalent… … Wikipedia
Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… … 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
Vector calculus — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus Derivative Change of variables Implicit differentiation Taylor s theorem Related rates … Wikipedia
Dual space — In mathematics, any vector space, V, has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V. Dual vector spaces defined on finite dimensional vector spaces can be used for defining tensors… … Wikipedia
Metric 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… … Wikipedia
Quadratic form — In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example, is a quadratic form in the variables x and y. Quadratic forms occupy a central place in various branches of mathematics, including… … Wikipedia
