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The word linear comes from the Latin word linearis, which means created by lines. In advanced mathematics, a linear map or function f(x) is a function which satisfies the following two properties:

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Wikipedia about linear

The word linear comes from the Latin word linearis, which means created by lines. In advanced mathematics, a linear map or function f(x) is a function which satisfies the following two properties:

  • Additivity (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 of degree 1: fx) = 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, provided that the function is continuous, it becomes useless to establish the condition of homogeneity as an additional axiom.

In this definition, x is not necessarily a real number, but can in general be a member of any vector space. A less restrictive definition of linear function, not coinciding with the definition of linear map, is used in elementary mathematics.

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 (or linear maps), and systems of linear equations.

Nonlinear equations and functions are of interest to physicists and mathematicians because they can be used to represent many natural phenomena, including chaos.

Integral linearity

For a device that converts a quantity to another quantity there are three basic definitions for integral linearity in common use: independent linearity, zero-based linearity, and terminal, or end-point, linearity. In each case, linearity defines how well the device's actual performance across a specified operating range approximates a straight line. Linearity is usually measured in terms of a deviation, or non-linearity, from an ideal straight line and it is typically expressed in terms of percent of full scale, or in ppm (parts per million) of full scale. Typically, the straight line is obtained by performing a least-squares fit of the data. The three definitions vary in the manner in which the straight line is positioned relative to the actual device's performance. Also, all three of these definitions ignore any gain, or offset errors that may be present in the actual device's performance characteristics.

Many times a device's specifications will simply refer to linearity, with no other explanation as to which type of linearity is intended. In cases where a specification is expressed simply as linearity, it is assumed to imply independent linearity.

Search results for Linear

Linear regression

Linear regression analyzes the relationship between two variables, X and Y. For ... In other cases, you use the linear regression line as a standard curve to find ...www.graphpad.com/curvefit/linear_regression.htm

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Linear Logic (Stanford Encyclopedia of Philosophy)

Linear logic is a refinement of classical and intuitionistic logic. ... To achieve this focus, linear logic does not allow the usual structural rules of ...plato.stanford.edu/entries/logic-linear/

Linear Programming FAQ

From the newsgroup sci.op-research, maintained at the Optimization Technology Center of ... The OR/MS Today 2005 Linear Programming Software Survey. ...www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.ht...

MIT OpenCourseWare | Mathematics | 18.06 Linear Algebra, Spring 2005 | Home

Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, ...ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/CourseHome/

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News about Linear

Coaxial resonator based VCO offers low phase noise in the UHF-band

Microwave Engineering OnlineSan Diego, CA — The ZRO0915C2LF from Z-Communications is an RoHS compliant coaxial resonator based VCO in the UHF-band that operates from 902- to 928-MHz with a linear tuning voltage range of 0 to 11 Vdc. The VCO delivers a typical phase noise of -128 dBc/Hz at 10 KHz offset and a typical tuning sensitivity of 3 MHz/V.http://www.mwee.com/210605489

Hell Girl Anime Debuts on IFC's Linear Channel Tonight

Anime News NetworkThe American cable television channel IFC will debut Studio DEEN 's first Hell Girl anime series on its linear channel tonight at 8:00 p.m. ET/PT. The 26-episode series had already premiered on IFC's video-on-demand service through Funimation earlier this year.http://www.animenewsnetwork.com/news/2008-09-30/hell-girl-an...

Linear Gold Provides Brazil Project Update

CCNMatthews via Yahoo! Finance HALIFAX, NOVA SCOTIA-- - Linear Gold Corp. is pleased to provide an update on the previously announced drill program at the El Filao project as well as on exploration activities conducted at the Serrinha project, both projects are located in the Alta Floresta gold province of northern Mato Grosso state, Brazil.http://biz.yahoo.com/ccn/080930/200809300488758001.html?.v=1

New Balluff Transducer Revitalizing Flight Simulators

ThomasNetBalluff announces a new linear position transducer designed especially for replacement of worn out or obsolete position feedback systems used by aircraft flight simulators. To provide a realistic flight experience, full flight simulators rely on very accurate and reliable closed-loop hydraulic servo control systems to provide necessary position feedback from their hydraulic cylinder legs. ...http://news.thomasnet.com/companystory/820286

Man's body found by hiker

Republican-AmericanPolice say a hiker on the Linear Park Trail found a man's body at about 6:30 p.m. Thursday, a few hundred yards east of Hillside Street in East Hartford. The man apparently has been dead for a long time.http://rep-am.com/articles/2008/10/02/news/doc48ca5793c9fae0...

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Refer to a friend

PR InsideSED's SRAM technology can successfully replace the crankshaft or swash plate in engines, pumps, motors, and compressors with a mechanism that converts linear to rotary, rotary to linear or linear to linear, replacing a combination of a crankshaft ... http://www.pr-inside.com/sanderson-engine-development-of-mas...

TOPEX and Therapy Remarketing Group Expand Distribution for Skin ...

PR NewswireTRG provides a unique mix of new and previously owned radiation therapy equipment including linear accelerators, CT-simulators, HDR and the TOPEX Superficial X-ray System.http://sev.prnewswire.com/health-care-hospitals/20080916/NYT...

Sign up for the Gamasutra Daily Newsletter!

GamasutraYou need to find somebody who's into this stuff -- somebody who's into non-linear music, and who's technical. I wouldn't feel comfortable throwing an essentially unfinished tool at who didn't feel comfortable with that situation.http://www.gamasutra.com/php-bin/news_index.php?story=20249

Linear Air Now Providing Maine Business and Leisure Travelers an ...

Magic City Morning StarCONCORD, MA -- The cutback of airline routes and increased fares are fueling travelers search for viable options to traditional travel offerings. Linear Air, a provider of point-to-point air service from the mid-Atlantic region through eastern Canada ... http://www.magic-city-news.com/State_18/Linear_Air_Now_Provi...

Government initiative champions advertising as a career

Brand RepublicSaid to be the culmination of a five-year project, Diagonal Thinking aims to validate the hypothesis that to get to the top in advertising you must be both a linear and lateral thinker.http://www.brandrepublic.com/News/846547/Government-initiati...

Search results for Linear

linear - Definitions from Dictionary.com

adjective . 1. of, consisting of, or using lines: linear design. 2. pertaining to or represented by lines: linear dimensions. 3. extended or arranged in a line: a linear series.http://dictionary.reference.com/search?q=linear

linear definition |Dictionary.com

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linear

linear1.org is a collection of material related to my various interests. You may find something here which interests you as well. Articles include case mods, electronics info ... http://linear1.org/

Linear Main

7-Aug-o8 Looking for Graphic Designers & Web Programmers. Interested in joining our team? Don't be shy. Email us at creative@linear.my or click here for more info.http://creative.linear.my/

Linear, Inc. TV Broadcast Transmitters | North America

Linear, Inc. manufactures digital low and medium power broadcast TV transmitters, made in the USA.http://linear-tv.com
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Algebra: Solving Linear Equations ?...

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Stanford's Linear Accelerator

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MIT Math Lecture: Linear Algebra - ...

MIT Math Lecture: Linear Algebra - 01 - The Geometry of Linear...MIT Math Lecture: Linear Algebra - 01 - The Geometry of Linear Equations 39 min 52 sec - Feb 10, 2007 01. The Geometry of Linear Equations These video lectures of Professor Gilbert Strang teaching 1...flash: 0 MB w:320px - h:266px

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Answers for Linear

keys_2_heaven

how do you determine linear footage? How should I determine the rate for installing greenboard drywall?

keys_2_heavenThere's a mail order company that I've gotten a catalog from in the past that sells the special measuring tool you need. Go to:www@easyliving.com to find it. Good luck to you.
mozzarella_24

How could I teach linear programming to my classmates in a creative way?

mozzarella_24Ummm .... use your classmates as the variables and constraints? I mean ... set up your presentation/problem the way you are going to ... write out on index cards (one variable or one constraint per...
Jake P

How do I find the linear function on several points of data?

Jake P
Beth

How do you find the linear equation with the TI-83 calculator?

Beththeres a button on the top left corner its Y= press that thenput in the equation of the line after that the GRAPH button is on the top right corner press it then ull get the graph
Jake S.

What is the difference between linear and exponential growth?

Jake S.Linear growth continues to increase at the same rate, whereas exponential growth increases at an expanding rate. Linear growth 1+1=2 2+1=3 3+1=4 4+5=6 ... Exponential Growth 1x2=2 2x...

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