There are bivectors such as that cannot be generated by the external product of two vectors.This also means they do not have a real, that is scalar, square.…
An attribute value is a specific valid value for the type of the attribute.This can be either a scalar value or a more complex type.A relation consists of a heading and a body.…
XLeratorDB uses three kinds of functions to perform analytic operations: scalar, aggregate, and a hybrid form which WestClinTech calls Range Queries.Scalar functions take a single value, perform an operation and return a single value.An example of this type of function is LOG, which returns the logarithm of a number to a specified base.…
It is these scalar-like properties which give rise to its name.
Among the unique new features in AVX-512F are instructions to decompose floating-point values and handle special floating-point values.Since these methods are completely new, they also exist in scalar versions.This is the second set of new floating-point methods, which includes new scaling and approximate calculation of reciprocal, and reciprocal of square root.…
Further, these properties are required to hold under any extension of scalars.
We see that while the scalar field remains the same, the vector field now looks different.The same holds even in the 1-dimensional case, as illustrated by the next example.…
With some care the scalar potential can be extended to include free currents as well.
This paper is also remarkable for the development of the idea of the scalar potential.The gravitational force acting on a body is, in modern language, a vector, having magnitude and direction.…
More subtly, scalar fields are often contrasted with pseudoscalar fields.In physics, scalar fields often describe the potential energy associated with a particular force.The force is a vector field, which can be obtained as the gradient of the potential energy scalar field.…
For example, a vector space comes with an associated field of scalar numbers.Let W and N denote the sort of vectors and numbers, respectively, let V W and V N be the set of vector and number variables, respectively, and C W and C N the set of vector and number constants, respectively.…
Specifically, the degree of a node is often a highly important feature in the mixing patterns of networks.Topological scalar features are very useful, because unlike other measures, they are always available.They are sometimes used as a proxy for real-world "sociability".…
The simplest calibration that can be performed on a network analyzer is a transmission measurement.This gives no phase information, and so gives similar data to a scalar network analyzer.The simplest calibration that can be performed on a network analyzer, whilst providing phase information is a 1-port calibration (S11 or S22, but not both).…
When the scalar field is the real numbers, the vector space is called a real vector space.When the scalar field is the complex numbers, it is called a complex vector space.These two cases are the ones used most often in engineering.…
Usually the system being modeled in this way is a chaotic dynamical system, because chaotic systems explore a large part of the phase space and the estimate of the global dynamics based on the local dynamics will be better than with a system exploring only a small part of the space.Frequently, one has only a single scalar time series measurement from a system known to have more than one degree of freedom.The time series may not even be from a system variable, but may be instead of a function of all the variables, such as temperature in a stirred tank reactor using several chemical species.…
A scalar holds a single value, such as a string, number, or reference to any other type.Arrays are ordered lists of scalars or complex types, indexed by number, starting at 1.…
These fields are the subject of scalar field theory.A vector field is an assignment of a vector to each point in a subset of space.…
When an anonymous inner class is defined within the body of a method, all variables declared final in the scope of that method are accessible from within the inner class.For scalar values, once it has been assigned, the value of the final variable cannot change.…
More generally, a vector space may be defined by using any field instead of real numbers, such as complex numbers.Then the scalars of that vector space will be the elements of the associated field.A scalar product operation may be defined on a vector space, allowing two vectors to be multiplied to produce a scalar.…
This idea is due to Strachey, but constants in many languages such as Pascal are manifest constants, processed at compile time and not implemented as protected locations.Also it must be possible to declare a constant of any data type, not just the scalar types.S-algol is an expression oriented language, and statements are expressions of type void.…