Sentence examples for a vector and a scalar from inspiring English sources

Hence, addition of a vector and a scalar adds the latter to each component of the former, and multiplications and divisions are performed component-wise on the operands, e.g., a k ∗ a k = [ (a 1 k ) 2, …, (a k k ) 2 ].

For the purposes of this article, the normal vector is defined as n = < A, B, C> where n is a vector, and A, B, and C are scalars.

In this case the slope is constant and it is not necessary to find a derivative to find the slope, which is, following the Y = mx + b basic model for linear graphs, 6. Displacement is like distance but it has a set direction, this makes displacement a vector and speed a scalar.

A fuzzy logic system is capable of mapping nonlinear relationships between an input vector and a scalar output; moreover it can handle both numerical values and human-like linguistic knowledge or variables.

Each of the identical Swarm satellites has a vector and scalar magnetometer, a Langmuir probe, an accelerometer, and GPS instrumentation on board, similar to the tremendously successful CHAMP satellite.

The following lemma provides a link between a vector ordering and a scalar ordering, which is a useful tool for reducing a vector problem to the scalar problem.

For example, if v is a vector and 2 is a scalar, then 2v is a vector in the same direction as v but twice as long.

This suggests a distinction between what we call potential efficacy (a vector) and realized efficacy (a scalar).

Therefore, we replace vector scalar division, in the form of (mathbf {x}/{alpha }) where (mathbf {x}) is a vector and (alpha) is a scalar, by vector scalar multiplication, in the form of (mathbf {x} cdot (1/{alpha })).

Let be a positive semidefinite matrix, let be a vector, and let be scalars.

But every one of them has an ancestor which is simply a function, not a vector, but a scalar function, an ordinary function of x and y.