scalar function in a sentence

Examples

1. As I'm sure you know, there are several alternative approaches  the field of analytical mechanics  that don't use forces, but scalar functions and a variational principle.
2. The gradient ( or gradient vector field ) of a scalar function is denoted or " f " } } where ( the nabla symbol ) denotes the vector differential operator, del.
3. A magnetic field is a vector field, but if it is expressed in Cartesian components, each component is the derivative of the same scalar function called the " magnetic potential ".
4. The Jacobian of the gradient of a scalar function of several variables has a special name : the Hessian matrix, which in a sense is the " second derivative " of the function in question.
5. The output of the network is then a scalar function of the input vector, \ varphi : \ mathbb { R } ^ n \ to \ mathbb { R }, and is given by
6. Because the electric field is irrotational, it is possible to express the electric field as the gradient of a scalar function, \ phi, called the electrostatic potential ( also known as the voltage ).
7. In many situations, the electric field is a conservative field, which means that it can be expressed as the gradient of a scalar function, that is,  & nabla; V } }.
8. The gradient of a scalar function ? is the vector field grad " f " that may be defined through the inner product \ langle \ cdot, \ cdot \ rangle on the manifold, as
9. Only in the simplest case ( coarse-graining, long-wavelength limit, cubic symmetry of the material ), these properties can be considered as ( complex-valued ) scalar functions of the frequency only.
10. For example, the second order partial derivatives of a scalar function of " n " variables can be organized into an " n " by " n " matrix, the Hessian matrix.