linear
UK /ˈlɪn.i.ə/ · US /ˈlɪn.i.əɹ/ adjective, proper noun
Forms linears
- adjective Having the form of a line; straight or roughly straight; following a direct course.
- adjective Of or relating to lines.
- adjective Made, or designed to be used, in a step-by-step, sequential manner. “a linear medium”
- adjective (botany, of leaves) Long and narrow, with nearly parallel sides.
- adjective (of a polynomial) Having degree one; that is, being of the form a_1x_1+a_2x_2+⋯+a_nx_n+b, where each x_i is a variable. See also Linear polynomials on Wikipedia.Wikipedia “4x#43;5y#43;#92;frac#123;1#125;#123;2#125;z is a linear polynomial, but 4xy#43;#92;frac#123;1#125;#123;2#125;z and 4x#43;z² are not.”
- adjective (of a polynomial equation) Involving only linear polynomials. See also Linear equation on Wikipedia.Wikipedia “The graph of the linear equation y#61;ax#43;b is a straight line with slope a and y-intercept b”
- adjective (of a function between vector spaces) An additive, homogeneous mapping; that is, a function f:V→W is linear if it distributes over vector addition (f( mathbf v+ mathbf w)=f( mathbf v)+f( mathbf w)) and respects scalar multiplication (f(c mathbf v)=cf( mathbf v)). If V and W are vector spaces over a field K, f may also be called a K-linear map. See also linear map on Wikipedia.Wikipedia “The map f#58;#92;mathbb#123;R#125;³#92;to#92;mathbb#123;R#125;² taking (x,y,z)#92;mapsto(x#43;y#43;z,x-y#43;3z) is a linear map.”
- adjective (of a function over a module) A module homomorphism; that is, a group homomorphism that commutes with scalar multiplication. See also Module homomorphism on Wikipedia.Wikipedia
- proper noun (astronomy) A comet, cataloged as “C/1999 S4”, discovered on September 27, 1999, by the Lincoln Near-Earth Asteroid Research program in New Mexico. (See https://web.archive.org/web/20051220100856/http://www.windows.ucar.edu/tour/link=/comets/linear.html) Sometimes spelled LINEAR.
Synonyms
lineal broadcast tune-in linelike additive one-dimensional analogue analog elongate running
Antonyms
Etymology
Borrowed from Latin līneāris, from līnea (“line”) + -āris (adjectival suffix), equivalent to line + -ar. Doublet of lineal.
Webster’s 1913
- adjective Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
- adjective Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf. Linear differential (Math.), an equation which is of the first degree, when the expression which is equated to zero is regarded as a function of the dependent variable and its differential coefficients.
Etymology [L. linearis, linearius , fr. linea line: cf. F. linéaire. See 3d Line.]
Sources: Wiktionary · WordNet 3.0 · Webster’s 1913 — from the Wiktionary entry “linear”, CC BY-SA 4.0. Details