Web Definition: Linear
The word linear comes from the Latin word linearis, which means created by lines. Additivity. f = f + f. Homogeneity. f = α f for all α. Systems that satisfy both additivity & homogeneity are considered to be linear systems. These two rules, taken together, are often referred to as the principle of superposition. In this definition, x is not necessarily a real number, but can in general be a member of any vector space. In the case that the field of scalars is the rationals or a finite field, superposition is enough to imply that they are from the same kind. However, in the case of the reals or complex numbers, both relations are needed. We are often concerned with bounded linear functions, which is equivalent to continuous ones. Although it is possible for a function to be linear & unbounded, these functions are usually of little practical importance. The concept of linearity can be extended to linear operators which are linear if they satisfy the superposition & homogenity relations.
Read More »Dictionary Entry: Of or pertaining to a line - consisting of lines - in a straight direction - lineal.
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