Inversion or inversions may refer to:

Arts

* ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas *

Inversion (music) In music theory, an inversion is a rearrangement of the top-to-bottom elements in an interval, a chord, a melody, or a group of contrapuntal lines of music. In each of these cases, "inversion" has a distinct but related meaning. The concept of i ...

, a term with various meanings in music theory and musical set theory * ''Inversions'' (novel) by Iain M. Banks * ''Inversion'' (video game), a 2012 third person shooter for Xbox 360, PlayStation 3, and PC * ''Inversions'' (EP), the 2014 extended play album by American rock music ensemble The Colourist * ''Inversions'' (album), a 2019 album by Belinda O'Hooley * ''Inversion'' (film), a 2016 Iranian film

Linguistics and language

Inversion (linguistics) In linguistics, inversion is any of several grammatical constructions where two expressions switch their typical or expected order of appearance, that is, they invert. There are several types of subject-verb inversion in English: ''locative inver ...

, grammatical constructions where two expressions switch their order of appearance * Inversion (prosody), the reversal of the order of a foot's elements in poetry *

Anastrophe Anastrophe (from the , ''anastrophē'', "a turning back or about") is a figure of speech in which the normal word order of the subject, the verb, and the object is changed. Anastrophe is a hyponym of the antimetabole, where anastrophe only transp ...

, a figure of speech also known as an ''inversion''

Mathematics and logic

Additive inverse In mathematics, the additive inverse of an element , denoted , is the element that when added to , yields the additive identity, 0 (zero). In the most familiar cases, this is the number 0, but it can also refer to a more generalized zero el ...

Involution (mathematics) In mathematics, an involution, involutory function, or self-inverse function is a function that is its own inverse, : for all in the domain of . Equivalently, applying twice produces the original value. General properties Any involution ...

, a function that is its own inverse (when applied twice, the starting value is obtained) *

Inversion (discrete mathematics) In computer science and discrete mathematics, an inversion in a sequence is a pair of elements that are out of their natural total order, order. Definitions Inversion Let \pi be a permutation. There is an inversion of \pi between i and j if ...

, any item that is out of order in a sequence *

Inverse element In mathematics, the concept of an inverse element generalises the concepts of opposite () and reciprocal () of numbers. Given an operation denoted here , and an identity element denoted , if , one says that is a left inverse of , and that ...

Inverse function In mathematics, the inverse function of a function (also called the inverse of ) is a function that undoes the operation of . The inverse of exists if and only if is bijective, and if it exists, is denoted by f^ . For a function f\colon ...

, a function that undoes the operation of another function. * Inversive geometry#Circle inversion, a transformation of the Euclidean plane that maps generalized circles to generalized circles * Inversion in a point, or

point reflection In geometry, a point reflection (also called a point inversion or central inversion) is a geometric transformation of affine space in which every point is reflected across a designated inversion center, which remains fixed. In Euclidean or ...

, a kind of isometric (distance-preserving) transformation in a Euclidean space *

Inversion transformation In mathematical physics, inversion transformations are a natural extension of Poincaré transformations to include all conformal map, conformal, bijection, one-to-one transformations on coordinate space-time. They are less studied in physics beca ...

, a conformal transformation (one which preserves angles of intersection) * Method of inversion, the image of a harmonic function in a sphere (or plane); see

Method of image charges The method of image charges (also known as the method of images and method of mirror charges) is a basic problem-solving tool in electrostatics. The name originates from the replacement of certain elements in the original layout with fictitious ...

Multiplicative inverse In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when Multiplication, multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a ra ...

, the reciprocal of a number (or any other type of element for which a multiplication function is defined) *

Matrix inversion In linear algebra, an invertible matrix (''non-singular'', ''non-degenarate'' or ''regular'') is a square matrix that has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can be multiplied by an ...

, an operation on a matrix that results in its multiplicative inverse *

Model inversion An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the ...

Set inversion In mathematics, set inversion is the problem of characterizing the preimage ''X'' of a set ''Y'' by a function ''f'', i.e., ''X'' = ''f''−1(''Y'' ) = . It can also be viewed as the problem of describing the solution set of the quantified c ...

Natural sciences

Biology and medicine

Inversion (evolutionary biology) In evolutionary developmental biology, inversion refers to the hypothesis that during the course of animal evolution, the structures along the anatomical terms of location, dorsoventral (DV) axis have taken on an orientation opposite that of the an ...

, a hypothesis about the evolution of the dorsoventral axis in animals *

Inversion (kinesiology) Motion, the process of movement, is described using specific anatomical terms. Motion includes movement of organs, joints, limbs, and specific sections of the body. The terminology used describes this motion according to its direction relativ ...

, movement of the sole towards the median plane *

Chromosomal inversion An inversion is a chromosome rearrangement in which a segment of a chromosome becomes inverted within its original position. An inversion occurs when a chromosome undergoes a two breaks within the chromosomal arm, and the segment between the two b ...

, where a segment of a chromosome is reversed end-to-end *

Inversion therapy Inversion therapy, or simply inversion, is the process of seeking therapeutic benefits from hanging by the legs, ankles, or feet in an inverted angle or entirely upside down. It is a form of spinal traction.Spinal Traction can be useful for eff ...

, the practice of hanging upside down (heart higher than head) for supposed health benefits

Geology

Inversion (geology) In structural geology, inversion or basin inversion relates to the relative uplift of a sedimentary basin or as a result of crustal shortening. This normally excludes uplift developed in the footwalls of later extensional faults, or uplift c ...

, the relative uplift of a previously basinal area resulting from local shortening, in structural geology *

Quartz inversion The room-temperature form of quartz, α-quartz, undergoes a reversible change in crystal structure at 573 °C to form β-quartz. This phenomenon is called an inversion, and for the α to β quartz inversion is accompanied by a linear expansion ...

, a change in the crystal structure of quartz at high temperatures *

Relief inversion Inverted relief, inverted topography, or topographic inversion refers to landscape features that have reversed their elevation relative to other features. It most often occurs when low areas of a landscape become filled with lava or sediment t ...

, when a previous depression becomes a landform that stands out from its surroundings *

Seismic inversion In geophysics (primarily in oil-and-gas exploration/development), seismic inversion is the process of transforming seismic reflection data into a quantitative rock-property description of a reservoir. Seismic inversion may be pre- or post- stack, ...

, transforming seismic reflection data into a quantitative rock-property description of a geological formation

Physics and chemistry

* Island of inversion, a group of elements with abnormal nuclear shell structure *

Nitrogen inversion In chemistry, pyramidal inversion (also umbrella inversion) is a fluxional process in compounds with a pyramidal molecule, such as ammonia (NH3) "turns inside out". It is a rapid oscillation of the atom and substituents, the molecule or ion pass ...

, a chemical process in which a trigonal nitrogen-containing structure turns inside-out *

Population inversion In physics, specifically statistical mechanics, a population inversion occurs when a system (such as a group of atoms or molecules) exists in a state in which more members of the system are in higher, excited states than in lower, unexcited energy ...

, in statistical mechanics, when a system exists in state with more members in an excited state than in lower-energy states *

Pyramidal inversion In chemistry, pyramidal inversion (also umbrella inversion) is a fluxional process in compounds with a pyramidal molecule, such as ammonia (NH3) "turns inside out". It is a rapid oscillation of the atom and substituents, the molecule or ion pass ...

, a chemical process in which a trigonal structure turns inside-out *

Inverted sugar syrup Inverted sugar syrup is a syrup mixture of the monosaccharides glucose and fructose, made by splitting disaccharide sucrose. This mixture's optical rotation is opposite to that of the original sugar, which is why it is called an ''invert'' sug ...

, a chemical reaction converting sucrose into glucose and fructose

Other uses in the natural sciences

Inverse problem An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, sound source reconstruction, source reconstruction in ac ...

, the process of calculating from a set of observations the causal factors that produced them *

Inversion (meteorology) In meteorology, an inversion (or temperature inversion) is a phenomenon in which a layer of warmer air overlies cooler air. Normally, atmospheric temperature, air temperature gradually decreases as altitude increases, but this relationship ...

, air temperature increasing with height

Other uses

Priority inversion In computer science, priority inversion is a scenario in scheduling in which a high-priority task is indirectly superseded by a lower-priority task, effectively inverting the assigned priorities of the tasks. This violates the priority model tha ...

, the condition of a low-priority task holding a shared resource that a high-priority task needs * Inversion in postcolonial theory, a discursive strategy/gesture in cultural and subaltern studies *

Roller coaster inversion A roller coaster inversion is a roller coaster element in which the track turns riders upside-down and then returns them to an upright position. Early forms of inversions were circular in nature and date back to 1848 on the Centrifugal railway in ...

, which turns riders upside-down *

Tax inversion A tax inversion or corporate tax inversion is a form of tax avoidance where a corporation restructures so that the current parent is replaced by a foreign parent, and the original parent company becomes a subsidiary of the foreign parent, thus mov ...

, a form of tax avoidance by moving corporate ownership to low-tax nations