Scalar Function Scalar Function In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector. 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 (not to be confused with scalar multiplication) may be defined on a vector space, allowing two vectors to be multiplied to produce a scalar. A vector space equipped with a scalar product is called an inner product space. The real component of a quaternion is also called its scalar part. The term is also sometimes used informally to mean a vector, matrix, tensor, or other usually "compound" value that is actually reduced to a single component.
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Thus, for example, the product of a 1×n matrix and an n×1 matrix, which is formally a 1×1 matrix, is often said to be a scalar. The term scalar matrix is used to denote a matrix of the form kI where k is a scalar and I is the identity matrix. Any function whose range is one dimensional is known as Scalar function. On other hand, a function whose range is three dimensional is known as vector function. Scalar valued function is defined as a function which returns a single value. This single value may be a string, integer, or any bit value. Scalar quantities can be explained through real life examples also like speed, distance are scalar quantities as they are one dimensional quantity and provides a specified result in a particular Domain over a specified range. Every function has its domain and range. Domain is defined as, set of values that can exist for a particular function and range is defined as, the set of values obtained on substituting the values of domain for which the function is defined. Scalar valued function is of various types like real Functions, complex Functions, real variable, scalar function and vector function. Real function: A function is said to be a real function if its range lies between Real Numbers that is negative infinite value to positive infinite value. Complex function: A complex function is defined as a function which contains real as well as imaginary numbers in its domain and range.
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Scalar function: Any function which contains one or more variable and its range is one dimensional is known as scalar function. Vector function: A function is said to be a vector function if it contains one or more variables and its range is three dimensional. Thus scalar functions and scalar valued function both are specified over a specific range.
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