Scalar valued Functions can be deterministic or non-deterministic. Scalar valued functions are mainly defined for scalar fields.
Following function is representing a scalar valued function:
P (a, b, c) = a2 + 2bc5
Output of scalar valued functions is actually Real Numbers.
Scalar field are those fields that usually deal with area of physical space (which is observable) with a function associated to it.
Scalar field can be defined as a field which assigns a value to each Point in space. Value, which Scalar Field assigns, is usually a scalar value. Scalar values may be any mathematical number or any physical quantity.
New scalar fields can be created by adjoining the existing scalar fields by using the algebraic operations.
Let ‘a’ and ‘b’ be scalar fields which are defined on same Domain and ‘c’ be scalar and ‘c’ is also a real number then scalar valued functions can be written as:
A1 (q) = c a (q),
A2 (q) = a (q) + b (q),
A3 (q) = a (q) b (q),
A4 (q) = a (q) / b (q),
When b (q) ≠ 0 then A1 (P), A2 (P), A3 (P), and A4 (P) will be scalar fields.
This is all about scalar valued functions.