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...

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...

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

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

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...

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"...

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...

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...

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

embedded in a Euclidean space. The normal vector space or normal space of a manifold at point P {\displaystyle P} is the set of vectors which are orthogonal...

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

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...

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...

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...

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...

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...

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

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

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...

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

reciprocal space or k space, which is the dual of physical space considered as a vector space, and the reciprocal lattice is the sublattice of that space that...

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

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

makes senses in metric spaces, and this gives rise to CAT(k) spaces. Curvature form for the appropriate notion of curvature for vector bundles and principal...

n-dimensional space, which, unlike the determinant of n vectors, is always positive, corresponding to a squared number. An orientation of a k-submanifold...

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

As with the term Euclidean space, the term pseudo-Euclidean space may be used to refer to an affine space or a vector space depending on the author, with...

orientability; see also Orientation of a vector bundle#Thom space.) Let p : E → B {\displaystyle p:E\to B} be a real vector bundle of rank n. Then there...