- adj.

- 直線的な、直鎖状の、リニアな、(数学)線形の、比例した

- measured lengthwise; "cost of lumber per running foot" (同)running
- designating or involving an equation whose terms are of the first degree (同)additive
- (of a leaf shape) long and narrow (同)elongate
- of or in or along or relating to a line; involving a single dimension; "a linear measurement" (同)one-dimensional
- give pleasant proportions to; "harmonize a building with those surrounding it"
- the relation between things (or parts of things) with respect to their comparative quantity, magnitude, or degree; "an inordinate proportion of the book is given over to quotations"; "a dry martini has a large proportion of gin" (同)ratio
- adjust in size relative to other things
- the quotient obtained when the magnitude of a part is divided by the magnitude of the whole
- magnitude or extent; "a building of vast proportions" (同)dimension
- harmonious arrangement or relation of parts or elements within a whole (as in a design); "in all perfectly beautiful objects there is found the opposition of one part to another and a reciprocal balance"- John Ruskin (同)proportionality, balance
- not homosexual
- a poker hand with 5 consecutive cards (regardless of suit)
- successive (without a break); "sick for five straight days" (同)consecutive
- characterized by honesty and fairness; "straight dealing"; "a square deal" (同)square
- erect in posture; "sit straight"; "stood defiantly with unbowed back" (同)unbent, unbowed
- (of hair) having no waves or curls; "her naturally straight hair hung long and silky"
- following a correct or logical method; "straight reasoning"
- free from curves or angles; "a straight line"
- having no deviations; "straight lines"; "straight roads across the desert"; "straight teeth"; "straight shoulders"
- in a straight line; in a direct course; "the road runs straight"
- in keeping with the facts; "set the record straight"; "made sure the facts were straight in the report"
- neatly arranged; not disorderly; "the room is straight now"
- in accordance with scientific laws
- being approximately average or within certain limits in e.g. intelligence and development; "a perfectly normal child"; "of normal intelligence"; "the most normal person I
*ve ever met"* - conforming with or constituting a norm or standard or level or type or social norm; not abnormal; "serve wine at normal room temperature"; "normal diplomatic relations"; "normal working hours"; "normal word order"; "normal curiosity"; "the normal course of events"
- forming a right angle
- having a constant ratio
- one of the quantities in a mathematical proportion
- properly related in size or degree or other measurable characteristics; usually followed by `to
*; "the punishment ought to be proportional to the crime"; "earnings relative to production" (同)relative* - in proportion; "the height of this wall must be reduced proportionately to give the room pleasant dimensions"
- in proportion (同)pro_rata
- to a proportionate degree; "your salary will rise proportionately to your workload" (同)proportionally
- being in due proportion; "proportionate representation of a minority group"
- agreeing in amount, magnitude, or degree
- a long slender leaf (同)elongate leaf
- mark with lines; "sorrow had lined his face"
- a length (straight or curved) without breadth or thickness; the trace of a moving point
- a single frequency (or very narrow band) of radiation in a spectrum
- reinforce with fabric; "lined books are more enduring"
- a particular kind of product or merchandise; "a nice line of shoes" (同)product line, line of products, line of merchandise, business line, line of business
- the road consisting of railroad track and roadbed (同)railway line, rail line
- a commercial organization serving as a common carrier
- acting in conformity; "in line with"; "he got out of line"; "toe the line"
- something (as a cord or rope) that is long and thin and flexible; "a washing line"
- a conceptual separation or distinction; "there is a narrow line between sanity and insanity" (同)dividing_line, demarcation, contrast
- a formation of people or things one behind another; "the line stretched clear around the corner"; "you must wait in a long line at the checkout counter"
- a formation of people or things one beside another; "the line of soldiers advanced with their bayonets fixed"; "they were arrayed in line of battle"; "the cast stood in line for the curtain call"
- a fortified position (especially one marking the most forward position of troops); "they attacked the enemy
*s line"* - a mark that is long relative to its width; "He drew a line on the chart"
- a spatial location defined by a real or imaginary unidimensional extent
- in games or sports; a mark indicating positions or bounds of the playing area
- persuasive but insincere talk that is usually intended to deceive or impress; "`let me show you my etchings
*is a rather worn line"; "he has a smooth line but I didn*t fall for it"; "that salesman must have practiced his fast line of talk" - text consisting of a row of words written across a page or computer screen; "the letter consisted of three short lines"; "there are six lines in every stanza"
- be in line with; form a line along; "trees line the riverbank" (同)run along
- cover the interior of; "line the gloves"; "line a chimney"
- fill plentifully; "line one
*s pockets"*

- 線の,直線の / 線から成る,線を使った;線状の / (方程式が)一次の
- 《the~》(…に対する…の)『割合』,比率《+『of』+『名』+『to』+『名』》 / 〈U〉(…との)『調和』,均衡《+『to』+『名』》 / 〈C〉部分;割り前,分け前 / 《複数形で》大きさ / 〈U〉比例 / …‘の'調和をとる;(…に)…‘を'釣り合わせる《+『名』+『to』+『名』》
- 『まっすぐな』,一直線の / (毛髪などが)まっすぐな / (背などが,曲らずに)『直立した』,まっすぐな / 《補語にのみ用いて》『整理した』,きちんとした / 真実を言う,率直な,正直な / 連続した / 《米》(ある政党に)徹底した,ベッタリの,きっすいの / (比較変化なし)『まっすぐに』,一直線に;『直立して』,垂直に / 『直ちに』,回り道をしないで / 率直に,端的に / 《the~》まっすぐ,一直線;直線コース / (カードゲームで)ポーカーの5枚続き,ストレート
- 『正常な』,『通常の』,標準の / (人が肉体・知能・情緒の発達において)平均的な,年齢相応の / (線などが)垂直な;(…に)垂直な《+『to』+『名』》・普通の;典型的な;直角をなす (to)・（実験動物が）常態の, 未処置［未免疫］の;（濃度が）規定の・常態;垂線, 法線;平均量［値］正常,通常;標準
- 比例の,比例による;(…と)比例として《+『to』+『名』》 / 釣り合った,調和した;(…に)釣り合った《+『to』+『名』》
- 釣り合いのとれた,比例した;(…と)釣り合いのとれた《+『to』+『名』》
- 『線』,筋,けい / (色・縫い目などの)『線』,しま;(顔・手などの)しわ(wrinkle) / (物・人の)『列』,行列(row) / 『綱』,糸,針金 / 電線,電話線,電信線 / (文章の)『行』;(詩の)『行』 / 《しばしばa~》《話》『短い手紙』(note) / 《複数形で》輪郭,外形(outline) / 境界線(boundary);限界,限度(limit) / (鉄道・バスなどの)路線;航路,空路 / 《複数形で》せりふ / 進路,道順(course);(考えなどの)筋道,方針 / 《しばしばone's~》(活動の)分野,方面;特意 / 家系,血統,血筋 / 在庫商品,仕入れ品 / 導管,パイプライン / 《しばしば複数形で》戦線,防御線 / …‘に'『線を引く』,筋(しま,しわ)をつける / …‘に'『沿って並ぶ;』(…を)…‘に'沿って並べる《+『名』+『with』+『名』》
- (材料で)〈着物など〉‘に'裏を付ける《+『名』『with』+『名』》 / (…で)…‘を'満たす,(…を)…‘に'詰め込む《+『名』+『with』+『名』》

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2017/02/27 20:45:43」(JST)

"Linear" redirects here. For other uses, see Linear (disambiguation).

Not to be confused with Lineage (disambiguation).

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (December 2007) (Learn how and when to remove this template message) |

**Linearity** is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line. Examples are the relationship of voltage and current across a resistor (Ohm's law), or the mass and weight of an object. Proportionality implies linearity, but linearity does not imply proportionality

- 1 In mathematics
- 1.1 Linear polynomials
- 1.2 Boolean functions

- 2 Physics
- 3 Electronics
- 3.1 Integral linearity

- 4 Military tactical formations
- 5 Art
- 6 Music
- 7 Measurement
- 8 See also
- 9 References
- 10 External links

In mathematics, a linear map or linear function *f*(*x*) is a function that satisfies the following two properties:^{[1]}

- Additivity:
*f*(*x*+*y*) =*f*(*x*) +*f*(*y*). - Homogeneity of degree 1:
*f*(α*x*) = α*f*(*x*) for all α.

The homogeneity and additivity properties together are called the superposition principle. It can be shown that additivity implies homogeneity in all cases where α is rational; this is done by proving the case where α is a natural number by mathematical induction and then extending the result to arbitrary rational numbers. If *f* is assumed to be continuous as well, then this can be extended to show homogeneity for any real number α, using the fact that rationals form a dense subset of the reals.

In this definition, *x* is not necessarily a real number, but can in general be a member of any vector space. A more specific 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 generally straightforward to solve by breaking the equation up into smaller pieces, solving each of those pieces, and summing the solutions.

Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear transformations (also called linear maps), and systems of linear equations.

The word **linear** comes from the Latin word *linearis*, which means *pertaining to or resembling a line*. For a description of linear and nonlinear equations, see *linear equation*. Nonlinear equations and functions are of interest to physicists and mathematicians because they can be used to represent many natural phenomena, including chaos.

Main article: linear equation

In a different usage to the above definition, a polynomial of degree 1 is said to be linear, because the graph of a function of that form is a line.^{[2]}

Over the reals, a linear equation is one of the forms:

- $f(x)=mx+b\$

where *m* is often called the slope or gradient; *b* the y-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 additivity or homogeneity. In fact, they do so if and only if *b* = 0. Hence, if *b* ≠ 0, the function is often called an **affine function** (see in greater generality affine transformation).

In Boolean algebra, a linear function is a function $f$ for which there exist $a_{0},a_{1},\ldots ,a_{n}\in \{0,1\}$ such that

- $f(b_{1},\ldots ,b_{n})=a_{0}\oplus (a_{1}\land b_{1})\oplus \cdots \oplus (a_{n}\land b_{n})$, where $b_{1},\ldots ,b_{n}\in \{0,1\}.$

A Boolean function is linear if one of the following holds for the function's truth table:

- In every row in which the truth value of the function is 'T', there are an odd number of 'T's assigned to the arguments and in every row in which the function is 'F' there is an even number of 'T's assigned to arguments. Specifically,
*f*('F', 'F', ..., 'F') = 'F', and these functions correspond to linear maps over the Boolean vector space. - In every row in which the value of the function is 'T', there is an even number of 'T's assigned to the arguments of the function; and in every row in which the truth value of the function is 'F', there are an odd number of 'T's assigned to arguments. In this case,
*f*('F', 'F', ..., 'F') = 'T'.

Another way to express this is that each variable always makes a difference in the truth-value of the operation or it never makes a difference.

Negation, Logical biconditional, exclusive or, tautology, and contradiction are linear functions.

In physics, *linearity* is a property of the differential equations governing many systems; for instance, the Maxwell equations or the diffusion equation.^{[3]}

Linearity of a differential equation means that if two functions *f* and *g* are solutions of the equation, then any linear combination *af* + *bg* is, too.

In instrumentation, linearity means that for every change in the variable you are observing, you get the same change in the output of the measurement apparatus - this is highly desirable in scientific work. In general, instruments are close to linear over a useful certain range, and most useful within that range. In contrast, human senses are highly nonlinear- for instance, the brain totally ignores incoming light unless it exceeds a certain absolute threshold number of photons.

In electronics, the linear operating region of a device, for example a transistor, is where a dependent variable (such as the transistor collector current) is directly proportional to an independent variable (such as the base current). This ensures that an analog output is an accurate representation of an input, typically with higher amplitude (amplified). A typical example of linear equipment is a high fidelity audio amplifier, which must amplify a signal without changing its waveform. Others are linear filters, linear regulators, and linear amplifiers in general.

In most scientific and technological, as distinct from mathematical, applications, something may be described as linear if the characteristic is approximately but not exactly a straight line; and linearity may be valid only within a certain operating region—for example, a high-fidelity amplifier may distort a small signal, but sufficiently little to be acceptable (acceptable but imperfect linearity); and may distort very badly if the input exceeds a certain value, taking it away from the approximately linear part of the transfer function.^{[4]}

Main article: Integral linearity

This section contains too-lengthy quotations for an encyclopedic entry. Please help improve the article by editing it to take facts from excessively quoted material and rewrite them as sourced original prose. Consider transferring direct quotations to Wikiquote. (September 2014) |

For an electronic device (or other physical device) that converts a quantity to another quantity, Bertram S. Kolts writes:^{[5]}^{[6]}

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.

Independent linearity is probably the most commonly used linearity definition and is often found in the specifications for DMMs and ADCs, as well as devices like potentiometers. Independent linearity is defined as the maximum deviation of actual performance relative to a straight line, located such that it minimizes the maximum deviation. In that case there are no constraints placed upon the positioning of the straight line and it may be wherever necessary to minimize the deviations between it and the device's actual performance characteristic.

Zero-based linearity forces the lower range value of the straight line to be equal to the actual lower range value of the device's characteristic, but it does allow the line to be rotated to minimize the maximum deviation. In this case, since the positioning of the straight line is constrained by the requirement that the lower range values of the line and the device's characteristic be coincident, the non-linearity based on this definition will generally be larger than for independent linearity.

For terminal linearity, there is no flexibility allowed in the placement of the straight line in order to minimize the deviations. The straight line must be located such that each of its end-points coincides with the device's actual upper and lower range values. This means that the non-linearity measured by this definition will typically be larger than that measured by the independent, or the zero-based linearity definitions. This definition of linearity is often associated with ADCs, DACs and various sensors.

A fourth linearity definition, absolute linearity, is sometimes also encountered. Absolute linearity is a variation of terminal linearity, in that it allows no flexibility in the placement of the straight line, however in this case the gain and offset errors of the actual device are included in the linearity measurement, making this the most difficult measure of a device's performance. For absolute linearity the end points of the straight line are defined by the ideal upper and lower range values for the device, rather than the actual values. The linearity error in this instance is the maximum deviation of the actual device's performance from ideal.

In military tactical formations, "linear formations" were adapted from phalanx-like formations of pike protected by handgunners towards shallow formations of handgunners protected by progressively fewer pikes. This kind of formation would get thinner until its extreme in the age of Wellington with the 'Thin Red Line'. It would eventually be replaced by skirmish order at the time of the invention of the breech-loading rifle that allowed soldiers to move and fire independently of the large-scale formations and fight in small, mobile units.

**Linear** is one of the five categories proposed by Swiss art historian Heinrich Wölfflin to distinguish "Classic", or Renaissance art, from the Baroque. According to Wölfflin, painters of the fifteenth and early sixteenth centuries (Leonardo da Vinci, Raphael or Albrecht Dürer) are more linear than "painterly" Baroque painters of the seventeenth century (Peter Paul Rubens, Rembrandt, and Velázquez) because they primarily use outline to create shape.^{[7]} Linearity in art can also be referenced in digital art. For example, hypertext fiction can be an example of nonlinear narrative, but there are also websites designed to go in a specified, organized manner, following a linear path.

In music the **linear** aspect is succession, either intervals or melody, as opposed to simultaneity or the vertical aspect.

In measurement, the term "linear foot" refers to the number of feet in a straight line of material (such as lumber or fabric) generally without regard to the width. It is sometimes incorrectly referred to as "lineal feet"; however, "lineal" is typically reserved for usage when referring to ancestry or heredity.[1] The words "linear"[2] & "lineal" [3] both descend from the same root meaning, the Latin word for line, which is "linea".

This section needs expansion. You can help by adding to it. (March 2013) |

- Linear actuator
- Linear element
- Linear system
- Linear medium
- Linear programming
- Linear differential equation
- Bilinear
- Multilinear
- Linear motor
- Linear A and Linear B scripts.
- Linear interpolation

**^**Edwards, Harold M. (1995).*Linear Algebra*. Springer. p. 78. ISBN 9780817637316.**^**Stewart, James (2008).*Calculus: Early Transcendentals*, 6th ed., Brooks Cole Cengage Learning. ISBN 978-0-495-01166-8, Section 1.2**^**Evans, Lawrence C. (2010) [1998],*Partial differential equations*(PDF), Graduate Studies in Mathematics,**19**(2nd ed.), Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-4974-3, MR 2597943**^**Whitaker, Jerry C. (2002).*The RF transmission systems handbook*. CRC Press. ISBN 978-0-8493-0973-1.**^**Kolts, Bertram S. (2005). "Understanding Linearity and Monotonicity" (PDF). analogZONE. Archived from the original (PDF) on February 4, 2012. Retrieved September 24, 2014.**^**Kolts, Bertram S. (2005). "Understanding Linearity and Monotonicity".*Foreign Electronic Measurement Technology*.**24**(5): 30–31. Retrieved September 25, 2014.**^**Wölfflin, Heinrich (1950). Hottinger, M.D., ed.*Principles of Art History: The Problem of the Development of Style in Later Art*. New York: Dover. pp. 18–72.

- The dictionary definition of linearity at Wiktionary

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

- 1. 表皮母斑および表皮母斑症候群 epidermal nevus and epidermal nevus syndrome
- 2. Sleep-wake disturbances and sleep disorders in patients with dementia
- 3. 線状IgA水疱性皮膚症 linear iga bullous dermatosis
- 4. 小児期の限局性強皮症 localized scleroderma in childhood
- 5. 小児における頭蓋骨骨折 skull fractures in children

- Linking N2O emission from biochar-amended composting process to the abundance of denitrify (nirK and nosZ) bacteria community.

- Li S1,2, Song L1, Jin Y1, Liu S1, Shen Q2, Zou J3,4.
- AMB Express.AMB Express.2016 Dec;6(1):37. doi: 10.1186/s13568-016-0208-x. Epub 2016 May 20.
- Manure composting has been recognized as an important anthropogenic source of nitrous oxide (N2O) contributing to global warming. However, biochar effect on N2O emissions from manure composting is rarely evaluated, especially by linking it to abundance of denitrifying bacteria community. Results of
- PMID 27207069

- Correlation between osteoporotic fracture risk in Brazilian postmenopausal women calculated using the FRAX with and without the inclusion of bone densitometry data.

- Bastos-Silva Y1, Aguiar LB1, Pinto-Neto AM1, Baccaro LF1, Costa-Paiva L2.
- Archives of osteoporosis.Arch Osteoporos.2016 Dec;11(1):16. doi: 10.1007/s11657-015-0255-y. Epub 2016 Apr 11.
- The risks of fracture were calculated in 402 postmenopausal Brazilian women by FRAX with or without the inclusion of bone densitometry values. The correlation between the risk of major osteoporosis fracture or hip fracture calculated by FRAX with or without BMD was similar in this population, 0.76 a
- PMID 27067597

- Phantom model and scoring system to assess ability in ultrasound-guided chest drain positioning.

- Vetrugno L1, Volpicelli G2, Barbariol F3, Toretti I4, Pompei L5, Forfori F6, Della Rocca G7.
- Critical ultrasound journal.Crit Ultrasound J.2016 Dec;8(1):1. doi: 10.1186/s13089-016-0038-8. Epub 2016 Feb 18.
- BACKGROUND: Chest tube positioning is an invasive procedure associated with potentially serious injuries. In the last few years, we have been running a project directed at developing a practical simulator of a surgical procedure taught on our medical training program. The phantom model reconstructs
- PMID 26888754

- CADA-computer-aided DaTSCAN analysis.

- Augimeri A1, Cherubini A2, Cascini GL3, Galea D4, Caligiuri ME5, Barbagallo G6, Arabia G7, Quattrone A8,9.
- EJNMMI physics.EJNMMI Phys.2016 Dec;3(1):4. doi: 10.1186/s40658-016-0140-9. Epub 2016 Feb 16.
- BACKGROUND: Dopamine transporter (DaT) imaging (DaTSCAN) is useful for the differential diagnosis of parkinsonian syndromes. Visual evaluation of DaTSCAN images represents the generally accepted diagnostic method, but it is strongly dependent on the observer's experience and shows inter- and intra-o
- PMID 26879864

- 鋼構造2層純骨組小模型の振動台実験の地震波加振レベルの違いによる応答比較

- 広島工業大学紀要. 研究編 42, 207-213, 39479-00-00
- NAID 120005403291

- 長周期地震動に対する中規模ブレース付鋼構造骨組の梁端部損傷度評価

- 日本建築学会構造系論文集 82(731), 115-122, 2017-01
- NAID 40021058749

- リニア駆動鉄道の最適省エネルギー運転曲線

- 電気学会論文誌. D, 産業応用部門誌 = IEEJ transactions on industry applications 137(1), 44-52, 2017-01
- NAID 40021058324

- リニアモータの電気-音響特性に基づく電力フィードバック型熱音響発電機の発振条件解析

- 日本音響学会誌 73(1), 12-20, 2017-01
- NAID 40021057669

- 拡張温度範囲 （HおよびMP）リニア・レギュレータ 拡張温度範囲（HおよびMP）スイッチング・レギュレータ 拡張温度範囲（HおよびMP）uModule レギュレータ 拡張温度範囲（HおよびMP）LEDドライバ 拡張温度範囲（HおよびMP ...

- プログレッシブ英和中辞典(第4版) - /línir/[形]1 直線状のa linear series｜1列に並んだもの.2 ((限定))長さの, 一次元の；線で表される.3 線からなる[を使った]；〈美術作品が〉線的な.4 線形の；糸状の, 細長いa linear design ...

- Linear Technology Corporation designs, manufactures and markets a broad line of standard high performance integrated circuits. Applications for the Company's products include telecommunications, cellular telephones, networking ...

リンク元 | 「normal」「比例」「proportional」「直鎖状」「proportionally」 |

拡張検索 | 「linearize」 |

関連記事 | 「line」 |

- adj.

- 関
- common、commonly、conventional、general、generally、in general、linear、N、n-、normally、ordinarily、ordinary、straight、usual、usually

- 英
- proportion、proportional、proportionate、linear、proportionally、proportionately
- 関
- 線形、直鎖状、比率、比例的、リニア、割合、直線的、釣り合い、釣り合った

- adj.

- 比例した(to)、釣り合った。比例の

- 関
- balanced、commensurable、commensurate、linear、proportion、proportionally、proportionate、proportionately、rate

- adv.

- 比例的に、比例して

- 直線化する

- n.

- v.

- 裏打ちする