Linear

Definitions: Linear

Linear

Adjective

1. (mathematics) directly proportional.

2. Of or in or along or relating to a line; involving a single dimension; "a linear foot".

3. (electronics) of a circuit or device having an output that is proportional to the input; "analogue device"; "linear amplifier".

4. Of a leaf shape; long and narrow.

5. Measured lengthwise; "cost of lumber per running foot".

Date "linear" was first used in popular English literature: sometime before 1550. (references)

Specialty Definitions: Linear

Domain	Definitions
Aerospace	1. Of or pertaining to a line.2. Having a relation such that a change in one quantity is accompanies by an exactly proportional change in a related quantity, such as input and output of electronic equipment. (references)
Computing	Qualifies a circuit having an output that varies in direct proportion to the input. Source: European Union. (references)
Math	(1) Any function which is a constant times the argument plus a constant: f(x)=c1x + c0. (2) In complexity theory, the measure of computation, m(n) (usually execution time or memory space), is bounded by a linear function of the problem size, n. More formally m(n) = O(n). (references)
Mining	Arranged in a line or lines; pertaining to the linelike character of someobject or objects.--n. Not recommended as a syn. of lineament. (references)
Post & Telecom	Pertaining to an operating characteristic, a device, an electrical network or a transmission medium satisfying the superposition principle according to which, within a specified working range at a specified output port, the signal resulting from an arbitrary input signal, applied to a given port is such that, when the input signal is increased by a numerical factor, the output signal is also increased by the same factor. Source: European Union. (references)
Science	Very narrow, with parallel margins. (references)
Statistics	The form of a relationship among variables such that when any two variables are plotted, a straight line results. A relationship is linear if the effect on a dependent variable of a change of one unit in an independent variable is the same for all possible such changes. Source: European Union. (references)
Source: compiled by the editor from various references; see credits.

Top

Specialty Definition: Linear

(From Wikipedia, the free Encyclopedia)

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):

Superposition: f(x + y) = f(x) + f(y)
Homogeneity: 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. In the case that the field of scalars is the rationals or a finite field, superposition is enough to imply homogeneity. 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 and 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 and homogenity relations. Examples of linear operators are del and the derivative function. 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.

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.

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.

In a slightly different usage to the above, a polynomial of degree 1 is said to be linear, because the graph of a function of that form is a line.

Over the reals, a linear function is one of the form:

f(x) = m x + c

m is often called the slope or gradient; c the intercept, which gives the point of intersection between the graph of the function and the y-axis.

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 superposition or homogeneity. In fact, they do so if and only if c = 0.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Linear."

Top

Abbreviations & Acronyms: Linear

The following table is compiled from various sources, across various languages. When English abbreviations or acronyms come from a non-English source, this is noted.
Entry	Source	Expression	Field
LINEAR	English	Lincoln Laboratory of Near-Earth Asteroid Research	Geography
LIB	English	Linear incremental backoff	N/A
Source: compiled by the editor, based on several corpora (additional references).

Top

Synonyms: Linear

Synonyms: additive (adj), analog (adj), analogue (adj), elongate (adj), one-dimensional (adj), running(a) (adj). (additional references)

Antonyms: cubic (adj), digital (adj), nonlinear (adj), planar (adj). (additional references)

Top

Synonyms within Context: Linear

Context	Synonyms within Context (source: adapted from Roget's Thesaurus).
Continuity	Adjective: continuous, continued; consecutive; progressive, gradual; serial, successive; immediate, unbroken, entire; linear; in a line, in a row; Noun: uninterrupted, unintermitting; unremitting, unrelenting (perseverence) a; perennial, evergreen; constant.
Length	Linear, lineal; longitudinal, oblong.
Paternity	Adjective: paternal, parental; maternal; family, ancestral, linear, patriarchal.
Source: adapted from Roget's Thesaurus.

Top

Crosswords: Linear

English words defined with "linear": linear accelerator, linear algebra, Linear numbers, linear programming ♦ metric linear unit, microwave linear accelerator ♦ nautical linear unit. (references)

Specialty definitions using "linear": Average planar linear heat generation rate ♦ best linear unbiased estimator, best linear unbiassed estimator ♦ constant linear velocity ♦ Digital Linear Tape, dual linear program ♦ integer linear program ♦ linear acceleration, linear address space, linear argument, linear assignment, linear density, linear foot, linear function, linear functions, Linear Graph Notation, linear induction motor, linear logic, linear map, Linear Models, linear optimization, linear PCM at 8 kHz, linear PEP, linear predictive coding, linear programing, linear space, linear transducer, linear type ♦ mixed integer linear program ♦ nearly best linear estimator ♦ piecewise linear encoding, Programming, Linear ♦ resultant linear density ♦ transistor linear peak envelope power rating. (references)

Etymologies containing "linear": Vertilinear. (references)

Non-English Usage: "Linear" is also a word in the following languages with English translations in parentheses.

Albanian (lineal, linear), German (in-line, linear, linearly, straight-line, unidimensional), Portuguese (lineal, linear, lineate), Turkish (linear).

Top

Modern Usage: Linear

Domain	Usage
Song Titles	Sending All My Love (performing artist: Linear)
Source: compiled by the editor from various references; see credits.

Top

Commercial Usage: Linear

Domain	Title
References	Micro Linear Corporation: International Competitive Benchmarks and Financial Gap Analysis (reference) Linear Technology Corporation: International Competitive Benchmarks and Financial Gap Analysis (reference) The World Market for Linear Acting Hydraulic Power Engines, Motors, and Cylinders: A 2004 Global Trade Perspective (reference) (more reference examples)

Books	Basic Operational Amplifiers and Linear Integrated Circuits (2nd Edition) (reference) Geometrical Methods for the Theory of Linear Systems: Proceedings of a NATO Advanced Study Institute and Ams Summer Seminar in Applied Mathematics, (reference) Linear Operators: Spectral Theory; Self Adjoint Operators in Helbert Space, Part 2 (Pure and Applied Mathematics, Vol 7) (reference) Operator Approach in Linear Problems of Hydrodynamics: Self-Adjoint Problems for an Ideal Fluid (Operator Theory, 128) (reference) The Adjoint of a Semigroup of Linear Operators (reference) (more book examples)

Periodicals	Linear Algebra & Its Applications (reference) Plastic Market Monthly - Linear Low Density Polyurethane (reference) (more periodical examples)

Theater & Movies	Drawing- Linear Perspective (reference) Linear Power Supplies (reference) Systems of Linear Equations Vol.4 (reference) (more DVD examples; more video examples)

Music	Cabled Linear Traction (reference) Linear Scaffold (reference) (more classical music examples; more popular music examples)

High Tech	Cokin Creative Filter A160 Linear Polarizer (reference) Cokin P160 Linear Polarizer Filter with Protective Case (reference) Tiffen 72mm Linear Polarizer (reference) 32MB LINEAR FLASH CARD-INTEL I SERIES (reference) LINEAR / NORTEK WI3P - Wireless Intercom (reference) (more camera examples; more video game examples; more computer examples; more electronic examples; more software examples)

Consumer Goods	Fetco International Wide Linear Frame, 4 X 6, Matted Rosewood (reference) Panasonic ES8003W Men's Wet/Dry Rechargeable Linear Shaver (reference) Panasonic ES8036N Men's Rechargeable Wet/Dry Shaver with High Speed Linear Motor (reference) (more baby examples; more wireless phone examples; more garden examples; more kitchen examples; more tool examples)
Source: compiled by the editor from various references; see credits.

Top

Image Slideshow: Linear

Top

Photo Album: Linear

Thumbnail	Description & Credit	Thumbnail	Description & Credit
	This is Gordon Isaacs, the first patient treated with the linear accelerator (radiation therapy) for retinoblastoma in 1957. Gordon's right eye was removed January 11, 1957 because the cancer had spread. His left eye, however, had only a localized tumor that prompted Henry Kaplan to try to treat it with the electron beam. Gordon is now living in the east bay, and his vision in the left eye is normal.Credit: Unknown photographer/artist.		Dr. Henry Kaplan, in the 1950's, with an early model of the Linear Accelerator developed to treat cancer. For this picture the protective hood was removed, revealing the electronic insides of the six-million volt machine, used for radiation treatment.Credit: Unknown photographer/artist.
	Test Firing of Linear Aerospike Engine.Credit: NASA.		Linear Aerospike SR-71 Experiment (LASRE).Credit: NASA.
	Lackluster comet LINEAR (C/1999 S4) unexpectedly threw astronomers a curve. Using the Hubble ...Credit: NASA.		Locust Bayou between plug site 7 and the existing southeast trending oil access canal. This 6500 linear foot section of Locust Bayou silted up and was dredged out to its natural depth prior to construction of the project's plugs.Credit: NOAA Restoration Center.
Source: compiled by the editor from various references; see credits.

Top

Familiar Quotations: Linear

Author	Quotation
Thomas Carlyle	Narrative is linear, but action has breadth and depth as well as height and is solid.
Source: compiled by the editor from various references.

Top

Non-Fiction Usage: Linear

Subject	Topic	Quote
Health		The longer linear opacities radiating from the lung hilum are known as Kerley A lines. (references)
		The chromosomes are made up of linear arrays of four chemicals, called bases, arranged in various sequence patterns. (references)
		These growths, which are often arranged in the same spiral or linear pattern as in the first stage, usually resolve during infancy or early childhood. (references)
Business		Equipment obsolescence regarding linear accelerator would indicate that at least each Argentine province would need to acquire new equipment. (references)
		Petrochema was established in 1949. Petrochema is a petrochemical company producing industrial oils and additives, detergents based on linear alkylbenzene sulphonates and sulphates of etoxyalcohols. (references)
		Sales of linear accelerators, gamma cameras, cobalt therapy systems, nuclear and non-nuclear diagnostic equipment, such as magnetic resonance imaging are generally limited to large medical centers specializing in radiology. (references)
Economic History	Mexico	There are 76 maritime ports in Mexico with 37,000 linear meters of pierage and docking facilities. (references)
	Colombia	Propylene, styrene, polyethylene of 0.94 gravity or more, polyethylene of less than 0.94, linear low-density, polypropylene, polyvinyl chloride, and polyesters are the best prospects for U.S. suppliers. (references)
	India	Systems like multi-parameters, ICCU, heart/lung machines, linear accelerators, Doppler, ultrasound machines, MRI scanners and other diagnostic and therapeutic equipment are showing good market potential. (references)
Source: compiled by the editor from ICON Group International, Inc.; see credits.

Top

Usage Frequency: Linear

"Linear" is generally used as an adjective (general or positive) -- approximately 97.23% of the time. "Linear" is used about 1,334 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted)

Parts of Speech	Percent	Usage per 100 Million Words	Rank in English
Adjective (general or positive)	97.23%	1,297	6,099
Noun (proper)	2.77%	37	56,631
Total	100.00%	1,334	N/A

Source: compiled by the editor from several corpora; see credits.

Top

Name Usage Frequency: Linear

The following table summarizes the usage of "linear" based on a population census conducted in the United States. Ranks and frequencies are based on all names reported and classified.

Name	Usage/Gender	Usage per 100 million Persons	Rank in USA
Linear	Last name	200	31,625
Source: compiled by the editor from several corpora; see credits.

Top

Usage in Company Names: Linear

Country	Name
USA	Linear Technology Corporation
	(more examples...)

Source: compiled by the editor from Icon Group International, Inc.

Top

Expressions: Linear

Expressions using "linear": adaptive linear element ♦ best linear unbiased estimator ♦ best linear unbiassed estimator ♦ constant linear velocity ♦ digital Linear Tape ♦ first order linear filter ♦ Geel Linear Accelerator ♦ linear a ♦ linear acceleration ♦ linear accelerator ♦ linear address space ♦ linear algebra ♦ linear amplification ♦ linear amplifier ♦ linear argument ♦ linear assignment ♦ linear b ♦ linear city ♦ linear codes ♦ linear combination of vectors ♦ linear combiner ♦ linear density ♦ linear detector ♦ Linear differential equation ♦ linear drawing ♦ linear energy transfer ♦ linear equation ♦ linear file ♦ linear foot ♦ linear function ♦ linear functions ♦ linear Graph Notation ♦ linear grid ♦ linear holding ♦ linear induction motor ♦ linear leaf ♦ linear light ♦ linear load ♦ linear logic ♦ linear map ♦ linear measure ♦ linear measurement ♦ Linear micrometer ♦ Linear Models ♦ linear momentum ♦ Linear numbers ♦ linear operator ♦ linear optimization ♦ linear pattern ♦ linear PCM at 8 kHz ♦ linear PEP ♦ linear perspective ♦ linear pit ♦ linear plan ♦ linear plot ♦ linear predictive coding ♦ Linear problem ♦ linear programing ♦ linear programming ♦ linear regression ♦ linear relationship ♦ linear sample plot ♦ linear scale ♦ linear shim ♦ linear space ♦ linear speed ♦ linear transformation ♦ linear type ♦ linear unit ♦ linear velocity ♦ metric linear unit ♦ microwave linear accelerator ♦ nautical linear unit ♦ nearly best linear estimator ♦ piecewise linear approximation ♦ piecewise linear encoding ♦ restricted linear collision stopping power ♦ resultant linear density ♦ transistor linear peak envelope power rating ♦ weir with linear flow characteristics. Additional references.
Hyphenated Usage
	Beginning with "linear": linear-quadratic, Linear-shaped.
	Ending with "linear": less-than-linear, log-linear, near-linear, non-linear, non-linear, piecewise-linear, quasi-linear, super-linear.
	Containing "linear": non-linear approach.
Source: compiled by the editor from various references; see credits.

Top

Frequency of Internet Keywords: Linear

The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com.

Expression	Frequency per Day	Expression	Frequency per Day
linear actuator	297	non linear editing	32
linear technology	257	graphing linear equation	29
linear	252	linear perspective	28
linear regression	162	linear interpolation	28
linear programming	156	linear encoders	28
linear equation	153	electric linear actuator	28
linear algebra	143	linear motion system	26
linear bearing	127	solving linear equation	25
linear motion	99	ceiling linear wood	25
linear motor	83	linear system	23
linear foot	81	linear potentiometer	22
linear tech	79	linear garage door opener	22
linear amplifier	62	linear programação	21
phase linear	54	simple linear regression	21
linear accelerator	49	linear encoder	20
linear slide	45	linear technology corp	20
multiple linear regression	37	linear induction motor	20
linear lighting	37	cb linear	20
linear function	35	linear transducer	19
linear power supply	33	linear measurement	18
Source: compiled by the editor from various references; see credits.

Top

Modern Translations: Linear

Language		Translations for "linear"; alternative meanings/domain in parentheses.
Albanian		linear (lineal), vizor, vijor, vijëdrejtë, i gjatë dhe i hollë (lanky, tall and thin). (various references)

Arabic		‏مؤلف من خطوط (lineal), ‏طولي (longitudinal), ‏خيطي (stringy), ‏خطي. (various references)

Bulgarian		линеен (lineal, marching, running), линеарен, продълговат (long, oblong), дълъг (long, long-spun, prolonged, protracted, straggling, tedious). (various references)

Chinese		线性 (linearity). (various references)

Czech		lineární, přímoèarý (straightforward). (various references)

Danish		lineaer, lineær sammenhæng (linear relationship), lineær, lineær. (various references)

Dutch		lineair. (various references)

Farsi		کشیده (Extensive, Long, Oblong, Taut), طولی , خطی (Lineal), دراز (Lengthy, Longish, Oblong, Prolix, String, Toom, Verbose), باریک (Capillary, Narrow, Slat, Slender, Slice, Strait, Tender, Tenuous, Thin). (various references)

Finnish		lineaarinen. (various references)

French		linéaire. (various references)

German		linear (in-line, linearly, straight-line, unidimensional). (various references)

Greek		γραμμικόσ, γραμμικός, επιμήκησ (elongate, oblong, slash). (various references)

Hebrew		מקווקו (lineal), מסורגל (laid, lined, ruled), שורתי, קוי (lined, ruled), סרגלני. (various references)

Hungarian		vonalas (banded, lineal, liny, ruled), lineáris, egyenes irányú (straightaway, straightforward). (various references)

Italian		lineare (coherent, logical, straightforward, unidimensional, unswerving). (various references)

Japanese Kanji		線状 , 線形 (line, straight alignment), リンク装置 (abuse, beating, bullying, conditioner, linkage, lymph, lynch, ring, ring binder, ring name, ring out, Ringer, ringside, rinse), リトマス試験紙 (linear motor, linear motorcar, linear programming, linen, linole, litmus paper, little, Little League, little magazine, Little Rock, Little Tokyo, rename, renewal, retractable, retractable headlamp, retry, rhythmic), 一次 (first, first-order, primary). (various references)

Japanese Katakana		リンネル , リニア , せんけい (design of a ship, fan shape, line, straight alignment, type of vessel), せんじょう (a streak, audacity, battlefield, battleground, cleaning, fan form, filament, forwardness, irrigation, line, rifling, sensational, suggestiveness, washing), いちじ (a character, a letter, a time, at one time, first, first-order, once, one hour, one thing, primary, short time, temporarily, twelfth part of a day). (various references)

Korean		선형. (various references)

Manx		linnagh. (various references)

Pig Latin		inearlay

Portuguese		linear (lineal, lineate). (various references)

Romanian		liniar (lineal, straight). (various references)

Russian		линейный (line, lineal, single-line). (various references)

Serbo-Croatian		linijski, linearan, vlaknast (fibriform, fibrillar), pravolinijski (rectilineal), dužinski (lengthwise, longitudinal). (various references)

Spanish		lineal (lineal). (various references)

Swedish		linjär. (various references)

Thai		เป็นเส้นตรง (lineal), โดยตรง (directly, due, right, straight, straightforward). (various references)

Turkish		linear, doğrusal, birinci derece, çizgisel (lineal). (various references)

Ukranian		схожий на лінію, лінійний (lineal). (various references)

Vietnamese		thuộc đường kẻ. (various references)
Source: compiled by the editor from various translation references.

Top

Ancestral Language Translations: Linear

Language	Period	Translations
Latin	500 BCE-Modern	linearis. (various references)
Source: compiled by the editor from various references.

Top

Derivations & Misspellings: Linear

Derivations
	Words beginning with "linear": linearise, linearised, linearises, linearising, linearities, linearity, linearization, linearizations, linearize, linearized, linearizes, linearizing, linearly. (additional references)
	Words ending with "linear": bilinear, colinear, collinear, curvilinear, interlinear, noncollinear, nonlinear, rectilinear, trilinear, unilinear. (additional references)
	Words containing "linear": colinearities, colinearity, collinearities, collinearity, curvilinearities, curvilinearity, interlinearly, interlinears, nonlinearities, nonlinearity, rectilinearly. (additional references)
Misspellings
	"Linear" is suggested in spellcheckers for the following: inea, inear, lenare, Leyenaar, Lienart, Liener, likeaaa, Limnaea, Linare, Linaria, lincean, Lindard, Lindegaard, linea, linead, linears, lineir, Linekars, linere, Lingara, lingera, Linha, Linhart, linii, linnear, Linnena, luniar, Lymnaea, minear, Pienaaar, pinear. (additional references)
Source: compiled by the editor, based on several corpora (additional references).

Top

Rhyming with "Linear"

# of Phoneme Matches	Pronunciation	Word(s) rhyming with "linear" (pronounced li"nēer)
4	-i" n ē er	skinnier.
3	-n ē er	funnier, pannier, tinier, vernier.
Source: compiled by the editor (additional references); see credits.

Top

Anagrams: Linear

Scrabble® Enable2K-Verified Anagrams
	Direct Anagrams: aliner, larine, nailer, renail.
	Words within the letters "a-e-i-l-n-r"
	-1 letter: alien, aline, anile, ariel, elain, learn, liane, liner, renal.
	-2 letters: airn, anil, aril, earl, earn, elan, ilea, lain, lair, lane, lari, lean, lear, liar, lien, lier, line, lira, lire, nail, near, rail, rain, rale, rani, real, rein, rial, riel, rile.
	-3 letters: ail, ain, air, ale, ane, ani, are, ear, era, ern, ire, lar.
	Words containing the letters "a-e-i-l-n-r"
	+1 letter: aileron, airline, aliener, alienor, aligner, aliners, carline, engrail, hernial, inhaler, inlayer, lankier, latrine, manlier, marline, mineral, nailers, nargile, plainer, praline, ralline, ratline, ravelin, realign, reginal, relaxin, reliant, renails, retinal, trenail.
	+2 letters: acrolein, ailerons, airliner, airlines, airplane, alerting, algerine, alieners, alienors, aligners, allergin, altering, auntlier, barnlike, bilander, bilinear, blearing, carlines, clarinet, clearing, colinear, dragline, elaterin, engrails, entailer, entrails, finagler, flanerie, fraulein, gainlier, ganglier, geranial, geraniol, germinal, gnarlier, grapline, hairline, hardline, hibernal, inarable, inertial, infernal, inflamer, inflater, inhalers, inhauler, inlander, inlayers, integral, interlap, interlay, internal, interval, irenical, islander, janglier, lagering, lanciers, latrines, layering, learning, linearly, maligner, malinger, marlines, minerals, mislearn, narghile, nargileh, nargiles, nearlier, oriental, overlain, pearling, pelorian, perineal, pralines, rainless, ratlines, raveling, ravelins, realigns, regaling, regional, relacing, relating, relation, relaxing, relaxins, relaying, reliance, renailed, retinals, retinula, rifleman, rinsable, ruinable, signaler, slangier, snarlier, tanglier, tenurial, terminal, tramline, trapline, treenail, trenails, triangle, triplane, valerian, yearling.
Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.