Science Fair Project Encyclopedia
The word linear comes from the Latin word linearis, which means created by lines.
- Additivity property: f(x + y) = f(x) + f(y).
- Homogeneity property: f(αx) = αf(x) for all α.
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.
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.
Over the reals, a linear function is one of the form:
- f(x) = m x + c
Note that this usage of the term linear is not the same as the above, because linear polynomials over the real numbers do not in general satisfy either additivity or homogeneity. In fact, they do so if and only if c = 0. Hence, if c ≠ 0, the function is often called an affine function (see in greater generality affine transformation).
- Linear medium
- Linear programming
- Linear motor
- Linear A and Linear B scripts.
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