The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented...

orientation of a real vector bundle is a generalization of an orientation of a vector space; thus, given a real vector bundle π: E →B, an orientation...

n-dimensional space is SO(n) × Rn. Orientation may be visualized by attaching a basis of tangent vectors to an object. The direction in which each vector points...

choice between them is an orientation of the space. Real vector spaces, Euclidean spaces, and spheres are orientable. A space is non-orientable if "clockwise"...

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied...

product vector. As the cross product operator depends on the orientation of the space, in general the cross product of two vectors is not a "true" vector, but...

fields, primarily in three-dimensional Euclidean space, R 3 . {\displaystyle \mathbb {R} ^{3}.} The term vector calculus is sometimes used as a synonym for...

mirror image Sinistral and dextral, terms in biology and geology Orientation (vector space), an asymmetry that makes a reflection impossible to replicate...

three-dimensional space, a surface normal, or simply normal, to a surface at point P is a vector perpendicular to the tangent plane of the surface at P. The vector field...

multiplication, it is a real vector space. The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension...

utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish...

Orientation (vector space), the specific case of linear algebra Orientability, a property of a geometrical space which allows choosing an orientation...

In mathematics, a symplectic vector space is a vector space V {\displaystyle V} over a field F {\displaystyle F} (for example the real numbers R {\displaystyle...

to be simply connected. Spatial vectors alone are not sufficient to describe fully the properties of rotations in space. Consider the following example...

vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length and direction denote the magnitude...

sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There...

length) and direction. Euclidean vectors can be added and scaled to form a vector space. A vector quantity is a vector-valued physical quantity, including...

In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance...

in space.: 154  Orbital state vectors come in many forms including the traditional Position-Velocity vectors, Two-line element set (TLE), and Vector Covariance...

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase...

wavenumbers k, known as reciprocal space or k space; it is the dual of physical space considered as a vector space. In other words, the reciprocal lattice...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space. Its length represents...

In mathematics, a set B of elements of a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite...

(physics) Enantiopure drug Enantioselective synthesis Handedness Orientation (vector space) Pfeiffer effect Stereochemistry for overview of stereochemistry...

convention is to be used at the beginning of each book or article. Orientation (vector space) Symmetry (physics) Gauge theory Negative logic Charles Misner;...

meaning in the group theory. Rotations of (affine) spaces of points and of respective vector spaces are not always clearly distinguished. The former are...

Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. They can also represent the orientation of a mobile frame of...

elements of a complex vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight...

viewed as a vector space with origin c. Let σ be any affine transformation of X. Pick a point c in X and consider the translation of X by the vector w = c σ...