Linear

:See also video-games)/">linearity (computer and video games)

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The word linear comes from the Latin word linearis, which means created by lines.

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In mathematics, a linear function f(x) is one which satisfies the following two properties (but see below for a slightly different usage of the term):

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• Additivity property (also called the superposition property): f(x + y) = f(x) + f(y). This says that f is a group isomorphism with respect to addition.
• Homogeneity property: f(αx) = αf(x) for all α.

In this definition, x is not necessarily a real number, but can in general be a member of any vector space.

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The concept of linearity can be extended to linear operators. Important examples of linear operators include the derivative considered as a differential operator, and many constructed from it, such as del and the Laplacian. When a differential equation can be expressed in linear form, it is particularly easy to solve by breaking the equation up into smaller pieces, solving each of those pieces, and adding the solutions up.

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Nonlinear equations and functions are of interest to physicists and mathematicians because they are hard to solve and give rise to interesting phenomena such as chaos.

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Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations.

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See also: linear element, linear system, nonlinearity.

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Function: In general (not in the mathematical but in the engineering sense), a function is a goal-oriented property of an entity. The carrier of a function is a process; therefore, is possible to realise the same function using different physical processes, and one process can be a carrier of multiple funct...

Real number: In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. The term "real number" is a retronym coined in response to "imaginary number"....

Vector space: A vector space (or linear space) is the basic object of study in the branch of mathematics called linear algebra....

Linear related Images and Photos (experimental)

Linear Poetry	Linear Motion I	Linear Motion IV	Linear Motion III
Linear Logic Blue I	Doctor Who Linear TARDIS	Doctor Who Linear TARDIS Babydoll	Doctor Who Linear TARDIS T-Shirt