Editing Asterisk (section)

===Mathematics===
The asterisk has many uses in [[mathematics]]. The following list highlights some common uses and is not exhaustive.

;stand-alone:
* An arbitrary point in some set. Seen, for example, when computing [[Riemann sums]] or when contracting a simply connected group to the singleton set <math>\{\ast\}</math>.
;as a [[unary operator]], denoted in [[prefix notation]]:
* The [[Hodge star operator]] on vector spaces <math>*: A^k \rightarrow A^{n-k}</math>.
;as a unary operator, written as a [[subscript]]:
* The [[pushforward (differential)]] of a [[smooth map]] <math>f</math> between two [[smooth manifolds]], denoted <math>f_*</math>.
* And more generally the application of any covariant [[functor]], where no doubt exists over which functor is meant. 
;as a unary operator, written as a [[superscript]]:
* The [[complex conjugate]] of a [[complex number]] (the more common notation is <math>\bar{z}</math>).<ref>{{cite web |url=http://mathworld.wolfram.com/ComplexConjugate.html |title=Complex Conjugate - from Wolfram MathWorld |publisher=Mathworld.wolfram.com |date=2018-09-12 |access-date=2018-09-18 |archive-date=2018-10-22 |archive-url=https://web.archive.org/web/20181022122115/http://mathworld.wolfram.com/ComplexConjugate.html |url-status=live }}</ref>
* The conjugate in a [[composition algebra]]
* The [[conjugate transpose]], Hermitian transpose, or adjoint matrix of a [[Matrix (mathematics)|matrix]].
* [[Hermitian adjoint]].
* The [[multiplicative group]] of the [[unit (ring theory)|units]] of a [[Ring (mathematics)|ring]]; when the ring is a [[Field (mathematics)|field]], this is the group of all nonzero elements. For example, <math>\mathbb{C}^* = \mathbb{C}\setminus\{0\}.</math>
* The [[dual space]] of a [[vector space]] <math>V</math>, denoted <math>V^*</math>.
* The combination of an indexed collection of objects into one example, e.g. the combination of all the [[cohomology|cohomology groups]] <math>H^k(X)</math> into the [[cohomology ring]] <math>H^*(X)</math>.
* The [[reflexive transitive closure]] of a [[binary relation]].
* In statistics, <math>z^*</math> and <math>t^*</math> are given critical points for <math>z</math>-distributions and <math>t</math>-distributions, respectively.
;as a [[binary operator]], in [[infix notation]]:
* A notation for an arbitrary binary operator.
* The [[free product]] of two [[Group (mathematics)|groups]].
* <math>f \ast g</math> is a [[convolution]] of <math>f</math> with <math>g</math>.
* A notation for the [[Natural transformation#Operations with natural transformations|horizontal composition]] of two natural transformations.
* A notation to denote a [[parallel sum]] of two operands (most authors, however, instead use a <math>:</math> or <math>\parallel</math> sign for this purpose).

The asterisk is used in all branches of mathematics to designate a correspondence between two quantities denoted by the same letter – one with the asterisk and one without.

====Mathematical typography====
In fine mathematical typography, the [[Unicode]] character {{unichar|2217|asterisk operator}} (in HTML, &amp;lowast;; not to be confused with {{unichar|204e|low asterisk}}) is available. This character also appeared in the position of the regular asterisk in the [[PostScript]] symbol character set in the ''Symbol'' font included with Windows and Macintosh operating systems and with many printers.{{citation needed|date=August 2024}} It should be used for a large asterisk that lines up with the other mathematical operators, sitting on the math centerline rather than on the text baseline.<ref>{{cite book |title=The Unicode Standard |edition=15.0 |chapter=Chapter 22: Symbols |pages=877-878 |year=2022 |url=https://www.unicode.org/versions/Unicode15.0.0/ch22.pdf |author=Unicode Consortium}}</ref>