# inverse

## Definitions

• WordNet 3.6
• adj inverse reversed (turned backward) in order or nature or effect
• adj inverse opposite in nature or effect or relation to another quantity "a term is in inverse proportion to another term if it increases (or decreases) as the other decreases (or increases)"
• n inverse something inverted in sequence or character or effect "when the direct approach failed he tried the inverse"
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Webster's Revised Unabridged Dictionary
• Inverse (Bot) Inverted; having a position or mode of attachment the reverse of that which is usual.
• Inverse (Math) Opposite in nature and effect; -- said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity; as, multiplication is the inverse operation to division. The symbol of an inverse operation is the symbol of the direct operation with -1 as an index. Thus sin-1x means the arc or angle whose sine is x.
• Inverse Opposite in order, relation, or effect; reversed; inverted; reciprocal; -- opposed to direct.
• n Inverse That which is inverse. "Thus the course of human study is the inverse of the course of things in nature."
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Century Dictionary and Cyclopedia
• inverse Turned end for end, or in the opposite direction; having a contrary course or tendency; inverted: opposed to direct.
• inverse In mathematics, opposite in nature and effect: said with reference to any two operations which, when both performed in succession upon the same quantity, leave it unaltered: thus, subtraction is inverse to addition, division to multiplication, extraction of roots to the raising of powers, etc. A direct operation produces an unambiguous and possible value, and between two operations the one which combines quantities symmetrically is preferably considered as direct. Addition, multiplication, involution, and differentiation are considered as direct operations; subtraction, division, evolution, and integration as inverse operations. Corresponding to every direct operation there are, generally speaking, two inverse operations: thus, if F(x, y) be the direct operation, the two inverse operations are the one which gives x from F(x, y) and y, and the one which gives y from F(x, y) and x.
• n inverse An inverted state or condition; a direct opposite; something directly or absolutely contrary to something else: as, the inverse of a proposition.
• inverse In logic, with conclusion as hypothesis and hypothesis as conclusion.
• n inverse In logic, a proposition made by simply interchanging the hypothesis and conclusion of another, without any restriction.
• n inverse In mathematics, an inverse point, curve, function, ratio, proportion, etc.
• n inverse In rouge-et-noir, the triangular space in which bets are placed when wagering that the first card dealt for a color will not be the same color as the one that wins the coup: opposed to couleur. See rouge-et-noir.
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Chambers's Twentieth Century Dictionary
• adj Inverse in-vėrs′ inverted: in the reverse or contrary order: opposite, inverted—opp. to Direct:
• n Inverse an inverted state, a direct opposite
• adj Inverse in-vėrs′ (math.) opposite in effect, of one operation that annuls the effect of another, as subtraction to addition, &c
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## Quotations

• Aldous Huxley
“Official dignity tends to increase in inverse ratio to the importance of the country in which the office is held.”
• C. Northcote Parkinson
“The Law of Triviality... briefly stated, it means that the time spent on any item of the agenda will be in inverse proportion to the sum involved.”
• Bertrand Russell
“The degree of one's emotions varies inversely with one's knowledge of the facts- the less you know the hotter you get.”
• Aldous Huxley
“The quality of moral behavior varies in inverse ratio to the number of human beings involved.”
• David Searles
“The tendency of an event to occur varies inversely with one's preparation for it.”
• Eric Hoffer
“The compulsion to take ourselves seriously is in inverse proportion to our creative capacity. When the creative flow dries up, all we have left is our importance.”

## Etymology

Webster's Revised Unabridged Dictionary
L. inversus, p. p. of invertere,: cf. F. inverse,. See Invert

## Usage

### In literature:

Also the further fact that its accuracy is in inverse ratio to its rapidity, which does not need so much explanation.
"Desert Conquest" by A. M. Chisholm
It takes him down a bit, and (inversely) elevates his rival.
"The House with the Green Shutters" by George Douglas Brown
The angle which the diameter of a heavenly body subtends at any time, varying inversely with its distance.
"The Sailor's Word-Book" by William Henry Smyth
Vary by inversion of the colors in ground and darker vase.
"A Color Notation" by Albert H. Munsell
We must now examine more closely the inversion whose consequences we have just described.
"Creative Evolution" by Henri Bergson
This communication was an inversion of that paradox.
"The Machine That Saved The World" by William Fitzgerald Jenkins
The tendency is to condemn the violation of these commandments, not in proportion to the injury done, but rather in inverse proportion.
"New York Times Current History; The European War, Vol 2, No. 4, July, 1915" by Various
After these come the women-folk in order of precedence, carrying loads in inverse ratio thereto.
"Pan-Islam" by George Wyman Bury
Now the dignity and virtue of the plates is in the exactly inverse ratio of their fullness in chiaroscuro.
But, inversely, if all art is concentrated upon the representation, what matters the subject?
This is sometimes a distressing symptom of the debility of the bowels joined with a partial inversion of their motions.
"Zoonomia, Vol. II" by Erasmus Darwin
The cost of filtering does not decrease in inverse ratio to the rate, but at a much slower rate.
"Transactions of the American Society of Civil Engineers, vol. LXXII, June, 1911" by E. D. Hardy
My pleasure was in like proportion, but inversely.
"The Wild Huntress" by Mayne Reid
This often requires inversion in the sentence.
"English: Composition and Literature" by W. F. (William Franklin) Webster
The inverse method was untried, and might well be deemed impracticable.
"A Popular History of Astronomy During the Nineteenth Century" by Agnes M. (Agnes Mary) Clerke
He had been a loner for so many years that he found a certain inverse pleasure in following someone else.
"Deathworld" by Harry Harrison
Some curious inversion of pride kept her silent on the subject of the change in her life.
"Turn About Eleanor" by Ethel M. Kelley
In fact, the people who talk so fluently about reaction fall back whenever it suits them upon the inverse theory.
"Hours in a Library" by Leslie Stephen
I would urge that this is the absolute inversion of the truth.
"New Worlds For Old" by Herbert George Wells
The duration of the contraction of the voluntary muscles, in some measure, is in an inverse ratio to its force.
"A Treatise on Anatomy, Physiology, and Hygiene (Revised Edition)" by Calvin Cutter
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### In news:

Norman Mailer , Warhol's Inverse, Helped Invent Modern Fame.
The worth of the personal finance industry is inversely proportional to its ubiquity, according to Forbes.com blogger Olen in his breezy romp through recent financial history.
INVERSE PRESETS USE THE SAME DEFAULT PRE-DELAY TIME.
Namco Bandai Games' new release, "Inversion," for the Xbox 360, PlayStation 3 and PC.
Peak error, integrated error, and rise time are inversely proportional to PID gain.
With all of its numerical symmetries, subdivisions and inversions, it could easily be the subject of a brainteaser from puzzle master Will Shortz.
Inversely, difficult short-term choices lead to easy long-term consequences.
Held in California and New York, the tests evaluated ways to recover people in the water and right dinghies from capsize and inversion.
What an inversion last night's vice presidential debate represented.
Set in Banks's far-future interstellar civilization known as the Culture, this highly literate novel from this celebrated British SF author ( Inversions ) centers on an act of revenge.
The post-WWII vision of a free Europe was hijacked by the ruling classes and gradually became the inversion of what was originally promised.
Inversion over the Wasatch Front Sunday, Dec 18, 2011 looking west from South Mounatin.
It also represents a fascinating, social-media-age inversion between the censor and the censored .
The investment seeks to replicate, net of expenses, three times the opposite (inverse) of the S&P GSCI Crude Oil Index ER.
Inversion layers have ups, downs.
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### In science:

It is clear that if f is a MP-inverse of e then e is a MP-inverse of f .
Moore-Penrose inverse, parabolic subgroups, and Jordan pairs
Baltes H P 1980 Progress in inverse optical problems, in Inverse Scattering Problems in Optics ed. H. P.
Design of one-dimensional Lambertian diffusers of light
We only need to prove that Φ is bijective with inverse Ψ on ob jects since Ψ is obviously the inverse of Φ on morphisms.
The categorical theory of relations and quantizations
We still have some uncertainty on the type inversion point. However from Fig. 12 we can see that, after type inversion, the slope is similar for both oxygenated and non-oxygenated sensors.
Characterization of Prototype BTeV Silicon Pixel Sensors Before and After Irradiation
For average connectivity greater than 1, the inverse participation ratio decreases with increasing N ; however, we do not observe a clear 1/N scaling of the inverse participation ratio for an average connectivity of 2.
Random Vibrational Networks and Renormalization Group
Jacobi’s theorem can also be used to ﬁnd the elements Ξij of the inverse reduced inverse matrix Ξ in (2.5), needed for (2.12).
Correlations and screening of topological charges in gaussian random fields
Here Di denotes the covariant derivative on the symmetric space and g ij are the components of the inverse of the metric tensor. (The metric has an inverse because it is non–degenerate on a semisimple algebra and can be mapped over the entire symmetric space.
Random matrix theory and symmetric spaces
The inverse image of ˜E ′ under G0 × ˜Y ′ −→ ˜Y ′ −→ ′ ˜Y equals f ∗ ˜E hence the inverse image of ′ q! ˜E ′ under G0 × Y ′ −→ Y ′ −→ ′Y ˜E ).
Character sheaves on disconnected groups, II
Let ˜F ′ be the local system on R′ whose inverse image under p1 : G0 ×UP ′ × c′ −→ R′ equals the inverse image of F ′ under p2 : G0 × UP ′ × c′ −→ c′ .
Character sheaves on disconnected groups, II
Since p1 , p2 are principal bundles with connected group it follows that the inverse image of I C (R, ˜F ′) under p1 : G0 × UP ′ × ¯c′ −→ R equals the inverse image of I C (¯c′ , F ′ ) under p2 : G0 × UP ′ × ¯c′ −→ ¯c′ .
Character sheaves on disconnected groups, II
This theory is not an inversion method for solving the inverse scattering problem.
Comments on the letter of P.Sabatier "An erroneous statement"
T denotes the determinant of T and eT is the inverse of the transpose of T , which is the same as the transpose of the inverse of T .
Elements of harmonic analysis, 2
Two models for the latter are considered: (1) an inverse potential (V ∝ 1 r ), where r is the distance between the center of the perturbation and the random walker and (2) an inverse of sixth power potential (V ∝ 1 r6 ).
Relaxation in open one-dimensional systems
The condition (3) has a remarkable property of being inversion invariant i.e. B ∗ and A may be replaced by their inverses.
Bounds for contractive semigroups and second order systems
Inversion automorphisms – Inv(∆) These include the involution ǫ : G(∆) → G(∆) such that ǫ(s) = s−1 for all s ∈ V (∆) , which we shall refer to as the global inversion of G(∆) , as well as the following involutions which we shall refer to as leaf inversions.
Automorphisms and abstract commensurators of 2-dimensional Artin groups
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