where are files stored in notational velocity

An example of a physical observable that does not change with a change of scale on the reference axes is the mass of a particle, which has units of mass (that is, no units of distance).

The components of a covector changes in the same way as changes to scale of the reference axes, and consequently is called covariant.Ī third concept related to covariance and contravariance is invariance. For example, a gradient which has units of a spatial derivative, or distance −1. In contrast, a covector, also called a dual vector, typically has units of the inverse of distance or the inverse of distance with other units.

As a result, a vector often has units of distance or distance with other units (as, for example, velocity has units of distance divided by time). A vector changes scale inversely to changes in scale to the reference axes, and consequently is called contravariant. For instance, by changing scale from meters to centimeters (that is, dividing the scale of the reference axes by 100), the components of a measured velocity vector are multiplied by 100. A change of scale on the reference axes corresponds to a change of units in the problem. In physics, a basis is sometimes thought of as a set of reference axes. In modern mathematical notation, the role is sometimes swapped. In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis. Note the basis and cobasis coincide only when the basis is orthogonal. A vector, v, represented in terms of tangent basis e 1, e 2, e 3 to the coordinate curves ( left), dual basis, covector basis, or reciprocal basis e 1, e 2, e 3 to coordinate surfaces ( right), in 3-d general curvilinear coordinates ( q 1, q 2, q 3), a tuple of numbers to define a point in a position space.

Where are files stored in notational velocity