coordinate vector

Also, the first parameter is assumed to be the x coordinate vector.

This process is very similar to the use of coordinates vector in linear algebra.

Let be the coordinate vector of an arbitrary point in the body with respect to the body-fixed frame.

Initially is also the space-fixed coordinate vector of .

The result of applying the outer product to a pair of coordinate vectors is a matrix.

The simplex in R with the vertices at the origin and along the unit coordinate vectors is normal.

The idea of a coordinate vector can also be used for infinite-dimensional vector spaces, as addressed below.

It corresponds to multiplying the coordinate vector by the transposed matrix:

Finally, assume that the material point under a small dynamic disturbance (acoustic stress field) have the coordinate vector .

The order of the basis becomes important here, since it determines the order in which the coefficients are listed in the coordinate vector.

When using affine transformations, the homogeneous component of a coordinate vector (normally called w) will never be altered.

The coordinate vector fields are both spacelike vector fields.

A group parameter is a component of a coordinate vector representing an arbitrary element of the Lie algebra with respect to some basis.

As the particle moves, its coordinate vector P(t) traces its trajectory, which is a curve in space, given by:

The lever is operated by applying an input force F at a point A located by the coordinate vector r on the bar.

To relate Brinkmann's definition to this one, take , the coordinate vector orthogonal to the hypersurfaces .

The position of a particle is defined to be the coordinate vector from the origin of a coordinate frame to the particle.

Coordinate vectors of finite-dimensional vector spaces can be represented by matrices as column or row vectors.

The vector of coordinates forms the coordinate vector or n-tuple (x, x, .

This equation for the trajectory of P can be inverted to compute the coordinate vector p in M as:

In pure mathematics, a vector is any element of a vector space over some field and is often represented as a coordinate vector.

On the other hand, when there is a fixed coordinate basis (or when not considering coordinate vectors), one may choose to use only subscripts; see below.

Recall that the trajectory of a particle P is defined by its coordinate vector P measured in a fixed reference frame F.

The coordinate vector field can be spacelike, null, or timelike at a given event in the spacetime, depending upon the sign of at that event.

The general formulation of covariance and contravariance refers to how the components of a coordinate vector transform under a change of basis (passive transformation).