In some cases the components of a vector may not be completely known.

The magnitude of the components of a vector are to be considered dimensionally distinct.

When the basis is changed, the components of a vector change by a linear transformation described by a matrix.

In quantum mechanics these three operators are the components of a vector operator known as angular momentum.

It seems that weak polarizations are ordinarily unable to form a component of a vector soliton.

The superscripts s and r denote the spatial and range components of a vector, respectively.

The function counting the number of non-zero components of a vector was called the "norm" by David Donoho.

The subscripts t and n refer to the tangential and normal components of a vector (with respect to the shock/discontinuity front).

In other words, the components of a vector transform contravariantly (with respect to the inverse) under a change of basis by the nonsingular matrix A.

We begin by finding out which component of a vector is being unfriendly to a second vector, which we may do with inner products.

Moreover, the radial and tangential components of a vector relate to the radius of rotation of an object.

The same techniques can be applied to similar problems, such as calculation of the component of a vector in a plane and perpendicular to the plane.

As an example, one can calculate the component of a vector perpendicular to a plane and the projection of that vector onto the plane.

As a linear transformation, the shift matrix "shifts" the components of a vector one position to the left, with a zero appearing in the last position:

To calculation the component of a vector outside of a plane we take the volume spanned by three vectors (trivector) and "divide out" the plane.

Within a given subspace, a component of a vector operator will behave in a way proportional to the same component of the angular momentum operator.

The first three values of the rotation field specify the X, Y and Z components of a vector which will be used as the rotation axis.

In an orthogonal co-ordinate system for a cubic cell, the Miller indices of a plane are the Cartesian components of a vector normal to the plane.

Conventionally, indices identifying the components of a vector are placed as upper indices and so are all indices of entities that transform in the same way.

Just as the components of a vector change when we change the basis of the vector space, the components of a tensor also change under such a transformation.

Recall that the x component of a vector is Rcos and the y component of a vector is Rsin.

The directional derivative Dv of the components of a vector v in a coordinate system φ in the direction u are replaced by a covariant derivative:

A terminology often used in physics refers to the curl-free component of a vector field as the longitudinal component and the divergence-free component as the transverse component.

The space of spin states therefore is a discrete degree of freedom consisting of three states, the same as the number of components of a vector in three-dimensional space.

While a vector is an objective quantity, meaning its identity is independent of any coordinate system, the components of a vector depend on what basis the vector is represented in.