# Vector

## Meanings and phrases

n.

- a variable quantity that can be resolved into components
- a straight line segment whose length is magnitude and whose orientation in space is direction
- any agent (person or animal or microorganism) that carries and transmits a disease; transmitter
- (genetics) a virus or other agent that is used to deliver DNA to a cell

n.

- a vector for delivering genes into cells; transducing vector

n.

- a gauge boson that mediates weak interactions between particles

n.

- a transducing vector that uses liposomes to carry the gene of interest

n.

- a line connecting a satellite to the center of the body around which it is rotating
- a line connecting a point in space to the origin of a polar coordinate system

n.

- a vector for delivering genes into cells; gene delivery vector

n.

- the part of algebra that deals with the theory of vectors and vector spaces

n.

- the analysis of a vector field; decomposition

n.

- a vector that is the product of two other vectors; cross product

n.

- a vector that is the sum of two or more other vectors; resultant

n.

- a transducing vector that uses a retrovirus

E.g.

- vector space, module) of all maps from into "X".
- This vector space is both Z-graded and R-graded.
- The annihilator of a subset is itself a vector space.

E.g.

- Consequently, the gradient determines a vector field.
- The velocity field u is the vector field to solve for.
- Let "v" be a vector field on "M" with isolated zeroes.

E.g.

- metric spaces) but not direction (such as vector spaces).
- Similar results hold for rings, modules, vector spaces, and algebras.
- Tangent spaces of differentiable manifolds are Euclidean vector spaces.

E.g.

- Equivalently, where are the coordinate vector fields.
- The curl is a form of differentiation for vector fields.
- If "r" = ∞, the space of vector fields is a Fréchet space.

E.g.

- A smooth manifold always carries a natural vector bundle, the tangent bundle.
- In particular, every smooth manifold has a canonical vector bundle, the tangent bundle.
- Every vector bundle of dimension formula_29 has a canonical formula_30-bundle, the frame bundle.

E.g.

- The unit vector basis of is not weakly Cauchy.
- where the hat indicates a unit vector in three dimensional space.
- As with u, u is a unit vector and can only rotate without changing size.

E.g.

- The arcade machine's monitor displayed vector graphics overlaying a holographic backdrop.
- The diagram plots deliver vector graphics which allows detailed result analysis in custom reports.
- In vector graphics, Bézier curves are used to model smooth curves that can be scaled indefinitely.

E.g.

- The sections define a morphism of vector bundles formula_14.
- "See also": analytic function, coherent sheaf and vector bundles.
- The following examples are defined for real vector bundles, particularly the tangent bundle of a smooth manifold.

E.g.

- The medium contains small optical absorbers moving with velocity vector formula_1.
- Speed, the scalar magnitude of a velocity vector, denotes only how fast an object is moving.
- The velocity of each point X is where ω is the angular velocity vector and v is the derivative of d("t").

E.g.

- Let "E" be a separable, real, topological vector space.
- At this time he was a leading expert in the theory of topological vector spaces.
- Let "X" and "Y" be locally convex topological vector spaces, and "U" ⊂ "X" an open set.

E.g.

- For example, given a real vector space, one can produce a complex vector space via complexification.
- The following examples are defined for real vector bundles, particularly the tangent bundle of a smooth manifold.
- Then "formula_26" and formula_29 are real vector spaces and the cotangent space is defined as the quotient space formula_34.

E.g.

- Let be a set in a real or complex vector space.
- Thus, for example, the two-dimensional complex vector space can be given a real structure.
- For example, given a real vector space, one can produce a complex vector space via complexification.

E.g.

- In other words, where is the magnitude of and is the unit tangent vector.
- an assignment to every point of the manifold "M" of a tangent vector to "M" at that point.
- This is the natural parameterization and has the property that where is a unit tangent vector.

E.g.

- Here "j" is the all-1 column vector of length "q" and "I" is the ("q"+1)×("q"+1) identity matrix.
- In an -dimensional Hilbert space, can be written as an column vector, and then is an matrix with complex entries.
- We assume that matrix equations of the form where g is a given column vector, can be solved directly for the vector x.