# Vector

### フレーズと例文

### vector space (ベクトル空間)

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.

### vector field (ベクトル場)

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.

### vector spaces (ベクトル空間)

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.

### vector fields (ベクトル場)

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.

### vector bundle (ベクトルバンドル)

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.

### unit vector

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.

### vector graphics

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.

### vector bundles (ベクトルバンドル)

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.

### velocity vector

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").

### topological vector

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.

### real vector

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.

### complex vector

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.

### tangent vector (接線ベクトル)

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.

### column vector

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.