different between inverse vs quadrature

English

Etymology

Recorded since 1440, from Latin inversus, the past participle of invertere (“to invert”), itself from in- (“in, on”) + vertere (“to turn”).

Pronunciation

• (General American) IPA^(key): /?n?v?s/, /??nv?s/

Adjective

inverse (not comparable)

1. Opposite in effect, nature or order.
2. Reverse, opposite in order.
3. (botany) Inverted; having a position or mode of attachment the reverse of that which is usual.
4. (mathematics) Having the properties of an inverse; said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity.

5. (geometry) That has the property of being an inverse (the result of a circle inversion of a given point or geometrical figure); that is constructed by circle inversion.

6. (category theory, of a category) Whose every element has an inverse (morphism which is both a left inverse and a right inverse).

Derived terms

• inverse function
• inverse image
• inverse spelling
• inversely
• inverse video

Related terms

• inversion
• inversive
• reverse

Translations

Noun

inverse (plural inverses)

1. An inverted state: a state in which something has been turned (properly) upside down or (loosely) inside out or backwards.

   Cowgirl is the inverse of missionary.

   321 is the inverse of 123.

2. The result of an inversion, particularly:
   1. The reverse of any procedure or process.

      Uninstalling is the inverse of installation.

   2. (mathematics) A ratio etc. in which the antecedents and consequents are switched.

      The inverse of a:b is b:a.

   3. (geometry) The result of a circle inversion; the set of all such points; the curve described by such a set.

      The inverse P‘ of a point P is the point on a ray from the center O through P such that OP × OP‘ = r² or the set of all such points.

   4. (logic) The non-truth-preserving proposition constructed by negating both the premise and conclusion of an initially given proposition.

      "Anything that isn't a dog doesn't go to heaven" is the inverse of "All dogs go to heaven." More generally, ${\displaystyle \lnot {\mathsf {p}}\to \lnot {\mathsf {q}}}$ is the inverse of ${\displaystyle {\mathsf {p}}\to {\mathsf {q}}}$ and is equivalent to the converse proposition ${\displaystyle {\mathsf {q}}\to {\mathsf {p}}}$.

      • 1896, James Welton, A Manual of Logic, 2nd ed., Bk iii, Ch. iii, §102:

        Inversion is the inferring, from a given proposition, another proposition whose subject is the contradictory of the subject of the original proposition. The given proposition is called the Invertend, that which is inferred from it is termed the Inverse... The rule for Inversion is: Convert either the Obverted Converse or the Obverted Contrapositive.

3. (mathematics) A second element which negates a first; in a binary operation, the element for which the binary operation—when applied to both it and an initially given element—yields the operation's identity element, specifically:
   1. (addition) The negative of a given number.

      The additive inverse of ${\displaystyle x}$ is ${\displaystyle -x}$, as ${\displaystyle x-x=0}$, as ${\displaystyle 0}$ is the additive identity element.

   2. (multiplication) One divided by a given number.

      The multiplicative inverse of ${\displaystyle x}$ is ${\displaystyle x^{-1}}$, as ${\displaystyle x\times x^{-1}=1}$, as ${\displaystyle 1}$ the multiplicative identity element.

   3. (functions) A second function which, when combined with the initially given function, yields as its output any term inputted into the first function.

      The compositional inverse of a function ${\displaystyle f}$ is ${\displaystyle f^{-1}}$, as ${\displaystyle f\ f^{-1}={\mathit {I}}}$, as ${\displaystyle {\mathit {I}}}$ is the identity function. That is, ${\displaystyle \forall x,f(f^{-1}(x))={\mathit {I}}(x)=x}$.

4. (category theory) A morphism which is both a left inverse and a right inverse.
5. (card games) The winning of the coup in a game of rouge et noir by a card of a color different from that first dealt; the area of the table reserved for bets upon such an outcome.
   • 1850, Henry George Bohn, The Hand-book of Games, p. 343:

     If the player... be determined to try his luck on the inverse, he must place his money on a yellow circle, or rather a collection of circles, situated at the extremity of the table.

   • 1950, Lawrence Hawkins Dawson, Hoyle's Games Modernized, 20th ed., p. 291:

     The tailleur never mentions the words ‘Black’ or ‘Inverse’, but always says that Red wins or Red loses, and that the colour wins or the colour loses.

6. (linguistics, Kiowa-Tanoan) A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.

Synonyms

• (addition): additive inverse
• (multiplication): multiplicative inverse
• (composition): compositional inverse
• (geometry): inverse point, inverse curve

Translations

See also

• (logic): obverse, converse, contraposition

Verb

inverse (third-person singular simple present inverses, present participle inversing, simple past and past participle inversed)

1. (surveying) To compute the bearing and distance between two points.

Antonyms

• compute (a point).

Anagrams

• Severin, enviers, inserve, veiners, venires, versine

Danish

Adjective

inverse

1. plural and definite singular attributive of invers

Dutch

Pronunciation

• Hyphenation: in?ver?se

Noun

inverse m or f (plural inversen)

1. inverse

Adjective

inverse

1. Inflected form of invers

Anagrams

• viseren

French

Pronunciation

• IPA^(key): /??.v??s/

Etymology 1

From Latin inversus.

Adjective

inverse (plural inverses)

1. inverse, the other way round

Derived terms

• barre inverse

• inversement

Noun

inverse m (plural inverses)

1. the inverse, the contrary

   Synonyms: contraire, envers

Derived terms

Etymology 2

Verb

inverse

1. first-person singular present indicative of inverser
2. third-person singular present indicative of inverser
3. first-person singular present subjunctive of inverser
4. third-person singular present subjunctive of inverser
5. second-person singular imperative of inverser

Further reading

• “inverse” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

Anagrams

• enivres, enivrés
• reviens
• Séverin
• vernies

German

Pronunciation

Adjective

inverse

1. inflection of invers:
   1. strong/mixed nominative/accusative feminine singular
   2. strong nominative/accusative plural
   3. weak nominative all-gender singular
   4. weak accusative feminine/neuter singular

Italian

Adjective

inverse

1. feminine plural of inverso

Anagrams

• svenire

Latin

Participle

inverse

1. vocative masculine singular of inversus

English

Etymology

Borrowed from Latin quadr?t?ra.

Pronunciation

• IPA^(key): /?kw?d.??.tj??(?)/, /-t???(?)/

Noun

quadrature (countable and uncountable, plural quadratures)

1. The process of making something square; squaring.
2. (mathematics) The act or process of constructing a square that has the same area as a given plane figure, or of computing that area.
   • 1976, D. T. Whiteside (editor), The Mathematical Papers of Isaac Newton, Volume 7: 1691-1695, Cambridge University Press, page 3,

     Craige was then on the point of publishing a short tract wherein he expounded a systematic (if far from general) 'Method of determining the quadrature of figures comprehended by straight lines and curves',^{[editor's translation]} there gathering a variety of techniques of rational algebraic quadrature and arc-rectification […] .

3. (mathematics, numerical analysis) The calculation of a definite integral by numerical means.
   • 1992, Bernard Bielecki, SINC Quadratures for Cauchy Principal Value Integrals, T.O. Espelid, Alan Genz, Springer, Numerical Integration: Recent Developments, Software and Applications, page 81,

     Three types of SINC quadratures are surveyed for the evaluation of Cauchy principal value integrals ${\displaystyle \textstyle \int _{\Gamma }F(t)dt/(t-x)}$, ${\displaystyle \textstyle x\in \Gamma }$, where ${\displaystyle \textstyle \Gamma }$ is an arc in the complex plane. Under suitable assumptions on F, the quadrature errors are of order ${\displaystyle \textstyle O(e^{-c{\sqrt {N}}})}$, where N is the number of quadrature nodes and c is a constant independent of N.

   • 2011, Narayan Kovvali, Theory and Applications of Gaussian Quadrature Methods, Morgan & Claypool, page 37,

     In this chapter, we present some example applications of the Gaussian quadrature methods discussed in the previous chapters. […] Figure 4.1 shows the accuracy of the polynomial Gaussian quadratures used to evaluate the first two integrals as a function of N.

   • 2015, Bernard Shizgal, Spectral Methods in Chemistry and Physics, Springer, page 71,

     The integral is thus given by a variant of the Fejér quadrature with two points at the interval boundaries, namely x₁ = ?1 and x_N = 1 analogous to the Lobatto quadratures of the next section.

4. (mathematics, mathematical analysis) The act or process of solving an indefinite integral by symbolic means.
5. (astronomy) A situation in which the directions of two celestial bodies (or a celestial body and the Sun) form a right-angle from the perspective of the observer.

6. (physics) The condition in which the phase angle between two alternating quantities is 90°.
   • 2008, Luis B. Oliveira, Jorge R. Fernandes, Igor M. Filanovsky, Chris J. M. Verhoeven, Manuel M. Silva, Analysis and Design of Quadrature Oscillators, Springer, page 33,

     If ?_IN has 50% duty-cycle, then the outputs are in quadrature.

   • 2011, M. V. Deshpande, Electrical Machines, PHI Learning, page 315,

     The total mmf in a synchronous machine may be split up into two components—one along the pole axis or direct axis and the other at right angles to this or the quadrature axis. […] In the case of salient pole construction, however, the reluctances of the magnetic circuits on which the mmfs act are different along the direct axis and the quadrature axis.

   • 2015, Mohammad Elbadry, Ramesh Harjani, Quadrature Frequency Generation for Wideband Wireless Applications, Springer, page 7,

     Quadrature LO generation is critical to the operation of direct-downconversion receivers [7]. Two common techniques for quadrature generation are divide-by-two frequency dividers, and polyphase filters.

7. (art) A painting painted on a wooden panel.

Derived terms

• add in quadrature
• differential quadrature
• Gaussian quadrature
• quadrature amplitude modulation
• quadrature domain

Related terms

• quadrate
• quadratural
• quadraturist

Translations

See also

• cubature
• square the circle

French

Etymology

Borrowed from Latin quadr?t?ra. Doublet of carrure.

Pronunciation

• IPA^(key): /ka.d?a.ty?/, /kwa.d?a.ty?/

Noun

quadrature f (plural quadratures)

1. quadrature

   quadrature du cercle – quadrature of the circle

Further reading

• “quadrature” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

Italian

Noun

quadrature f

1. plural of quadratura

Latin

Participle

quadr?t?re

1. vocative masculine singular of quadr?t?rus