Adjoint vs. Inverse — What's the Difference?

In mathematics, the term adjoint applies in several situations.

Reversed in order, nature, or effect.

(mathematics) Used in certain contexts, in each case involving a pair of transformations, one of which is, or is analogous to, conjugation (either inner automorphism or complex conjugation).

(Mathematics) Of or relating to an inverse or an inverse function.

That is related to another functor by an adjunction.

(Archaic) Turned upside down; inverted.

Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.

Something that is opposite, as in sequence or character; the reverse.

(mathematics) The transpose of the cofactor matrix of a given square matrix.

The reciprocal of a designated quantity. Also called multiplicative inverse.

Transpose conjugate.

The negative of a designated quantity. Also called additive inverse.

Hermitian conjugate.

Opposite in effect, nature or order.

A functor related to another functor by an adjunction.

Reverse, opposite in order.

A curve A such that any point of a given curve C of multiplicity r has multiplicity at least r–1 on A. Sometimes the multiple points of C are required to be ordinary, and if this condition is not satisfied the term sub-adjoint is used.

(botany) Inverted; having a position or mode of attachment the reverse of that which is usual.

An assistant to someone who holds a position in the military or civil service.

(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.

An assistant mayor of a French commune.

(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. Category:en:Curves

An adjunct; a helper.

Whose every element has an inverse (morphism which is both a left inverse and a right inverse).

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

The result of an inversion, particularly:

The reverse of any procedure or process.

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

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

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

(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:

(addition) The negative of a given number.

(multiplication) One divided by a given number.

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

(category theory) A morphism which is both a left inverse and a right inverse.

(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.

A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.

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

Opposite in order, relation, or effect; reversed; inverted; reciprocal; - opposed to direct.

Inverted; having a position or mode of attachment the reverse of that which is usual.

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-1 x means the arc or angle whose sine is x.

That which is inverse.

Something inverted in sequence or character or effect;

Reversed (turned backward) in order or nature or effect

Opposite in nature or effect or relation to another quantity ;