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searching for Euclidean vector 32 found (82 total)

Pseudo-Riemannian manifold (1,171 words) [view diff] exact match in snippet view article find links to article

relaxed. Every tangent space of a pseudo-Riemannian manifold is a pseudo-Euclidean vector space. A special case used in general relativity is a four-dimensional

Null vector (582 words) [view diff] exact match in snippet view article find links to article

anisotropic space for a quadratic space without null vectors. A pseudo-Euclidean vector space may be decomposed (non-uniquely) into orthogonal subspaces A

Reflection (mathematics) (1,154 words) [view diff] exact match in snippet view article

1969, §7.2), and exhibits Euclidean space as a symmetric space. In a Euclidean vector space, the reflection in the point situated at the origin is the same

Symplectic vector space (2,275 words) [view diff] exact match in snippet view article find links to article

differently from a symmetric form, for example, the scalar product on Euclidean vector spaces. The standard symplectic space is R 2 n {\displaystyle \mathbb

Perfect lattice (478 words) [view diff] exact match in snippet view article find links to article

mathematics, a perfect lattice (or perfect form) is a lattice in a Euclidean vector space, that is completely determined by the set S of its minimal vectors

Normed vector space (2,890 words) [view diff] exact match in snippet view article find links to article

the inner product of a vector and itself. The Euclidean norm of a Euclidean vector space is a special case that allows defining Euclidean distance by

Norm (mathematics) (5,957 words) [view diff] exact match in snippet view article

distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the Euclidean norm, the 2-norm, or, sometimes, the magnitude

Quasi-sphere (1,144 words) [view diff] exact match in snippet view article find links to article

This article uses the following notation and terminology: A pseudo-Euclidean vector space, denoted Rs,t, is a real vector space with a nondegenerate quadratic

Conformal linear transformation (790 words) [view diff] exact match in snippet view article find links to article

similitude, is a similarity transformation of a Euclidean or pseudo-Euclidean vector space which fixes the origin. It can be written as the composition

Complex number (11,603 words) [view diff] exact match in snippet view article find links to article

algebraically closed field, a commutative algebra over the reals, and a Euclidean vector space of dimension two. A complex number is an expression of the form

Orthogonal group (7,856 words) [view diff] exact match in snippet view article find links to article

originates from the following characterization of its elements. Given a Euclidean vector space E of dimension n, the elements of the orthogonal group O(n) are

Formal calculation (885 words) [view diff] exact match in snippet view article find links to article

positively oriented orthonormal basis of a three-dimensional oriented Euclidean vector space, while a 1 , a 2 , a 3 , b 1 , b 2 , b 3 {\displaystyle a_{1}

Rigid transformation (1,146 words) [view diff] exact match in snippet view article find links to article

of Euclidean spaces, while the sections describe only the case of Euclidean vector spaces or of spaces of coordinate vectors. The "formal definition"

Real projective line (1,667 words) [view diff] exact match in snippet view article find links to article

the differential structure. These are solved by considering V as a Euclidean vector space. The circle of the unit vectors is, in the case of R2, the set

Semidefinite embedding (1,572 words) [view diff] exact match in snippet view article find links to article

mapping from the high dimensional input vectors to some low dimensional Euclidean vector space in the following steps: A neighbourhood graph is created. Each

Number line (2,543 words) [view diff] exact match in snippet view article find links to article

It has the usual multiplication as an inner product, making it a Euclidean vector space. The norm defined by this inner product is simply the absolute

Axis–angle representation (2,117 words) [view diff] exact match in snippet view article find links to article

named after Olinde Rodrigues, is an efficient algorithm for rotating a Euclidean vector, given a rotation axis and an angle of rotation. In other words, Rodrigues'

Complex plane (4,502 words) [view diff] exact match in snippet view article find links to article

view of the complex numbers is implicitly based on its structure of a Euclidean vector space of dimension 2, where the inner product of complex numbers w

Multiplication (music) (2,099 words) [view diff] exact match in snippet view article

retrograde, and retrograde-inverse—operations of matrix multiplication in Euclidean vector space—but also their rhythmic counterparts as well. Thus he could describe

Hedgehog (geometry) (1,482 words) [view diff] exact match in snippet view article

convex bodies: given (K,L) an ordered pair of convex bodies in the Euclidean vector space R n + 1 {\displaystyle \mathbb {R} ^{n+1}} , there exists one

Triangle inequality (5,175 words) [view diff] exact match in snippet view article find links to article

inner product is norm in any inner product space, a generalization of Euclidean vector spaces including infinite-dimensional examples. The triangle inequality

Brauer algebra (2,655 words) [view diff] exact match in snippet view article find links to article

length formula. Let V = R d {\displaystyle V=\mathbb {R} ^{d}} be a Euclidean vector space of dimension d {\displaystyle d} , and O ( V ) = O ( d , R )

Sine and cosine (6,966 words) [view diff] exact match in snippet view article find links to article

The cross product and dot product are operations on two vectors in Euclidean vector space. The sine and cosine functions can be defined in terms of the

Riemann integral (5,360 words) [view diff] exact match in snippet view article find links to article

easy to extend the Riemann integral to functions with values in the Euclidean vector space R n {\displaystyle \mathbb {R} ^{n}} for any n. The integral

Manifold (9,511 words) [view diff] exact match in snippet view article find links to article

which is such that the group operations are defined by smooth maps. A Euclidean vector space with the group operation of vector addition is an example of

Root system (6,237 words) [view diff] exact match in snippet view article find links to article

root system; this one is known as A2. Let E be a finite-dimensional Euclidean vector space, with the standard Euclidean inner product denoted by ( ⋅ , ⋅

Poincaré half-plane model (3,972 words) [view diff] exact match in snippet view article find links to article

space by replacing the real number x by a vector in an n dimensional Euclidean vector space. Angle of parallelism Anosov flow Fuchsian group Fuchsian model

Quantum field theory (14,793 words) [view diff] exact match in snippet view article find links to article

infinite) dimension in the category of Banach spaces (though still their Euclidean vector space dimension is uncountable), so in these restricted contexts, the

Topological vector space (13,537 words) [view diff] exact match in snippet view article find links to article

Euclidean topology, and then the infinitely many remaining non-trivial non-Euclidean vector topologies on X {\displaystyle X} are all TVS-isomorphic to one another

List of trigonometric identities (12,426 words) [view diff] exact match in snippet view article find links to article

properties of the trigonometric functions. When the direction of a Euclidean vector is represented by an angle θ , {\displaystyle \theta ,} this is the

Near sets (9,533 words) [view diff] exact match in snippet view article find links to article

where R n {\displaystyle \mathbb {R} ^{n}} is an n-dimensional real Euclidean vector space. Φ ( x ) {\displaystyle \Phi (x)} is a feature vector for x {\displaystyle

Area of a triangle (3,530 words) [view diff] exact match in snippet view article find links to article

^{2}\mathbf {c} ^{2}-(\mathbf {b} \cdot \mathbf {c} )^{2}}},} where for any Euclidean vector v 2 = ‖ v ‖ 2 = v ⋅ v {\displaystyle \mathbf {v} ^{2}=\|\mathbf {v}