linear
adj.
straight; one dimensional; pertaining to length; involving or resembling lines; narrow and elongated; involving linear functions or equations (Mathematics)
Linear
For other uses, see Linear (disambiguation)}}}. The word linear comes from the
Latin word linearis, which means created by lines. 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):Additivity property (also called the
superposition property): f(x + y) = f(x) + f(y). This says that f is a
group homomorphism with respect to addition.Homogeneity property: f(αx) = αf(x) for all α. It turns out that homogeneity follows from the additivity property in all cases where α is rational. In that case if the linear function is continuous, homogeneity is not an additional axiom to establish if the additivity property is established.
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linear
Adjective
1. designating or involving an equation whose terms are of the first degree
(synonym) additive
(antonym) nonlinear
(similar) bilinear
(classification) mathematics, math, maths
2. of or in or along or relating to a line; involving a single dimension; "a linear foot"
(synonym) one-dimensional
(antonym) planar, two-dimensional
(similar) collinear
3. of a circuit or device having an output that is proportional to the input; "analogue device"; "linear amplifier"
(synonym) analogue, analog
(classification) electronics
4. of a leaf shape; long and narrow
(synonym) elongate
(similar) simple, unsubdivided
5. measured lengthwise; "cost of lumber per running foot"
(synonym) running(a)
(similar) lengthwise, lengthways
linear
adj.
linear, straight; pertaining to length; involving or resembling lines; involving linear functions or equations (Mathematics)
adv.
linearly, in the manner of a straight line
linear
adj.
lineal, linear