Star and asterisk (⋆ ∗) in LaTeX
\star and \ast produce the star (⋆) and asterisk (∗) operators, general-purpose symbols used for convolution, complex conjugates, adjoints and other 'starred' variants of an object.
LaTeX command
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\star is typically used as a genuine binary operator between two symbols, most recognisably for convolution in signal processing, , though texts also use it as a placeholder for any abstract operation, much like \circ.
A superscript asterisk, as in z^{*} or A^{*}, is the more common pattern for 'starring' a single object: a complex conjugate, an adjoint operator, or a dual space V^{*}. This is a modifier attached to one symbol, not a relation between two, so it belongs in the exponent position rather than inline.
\ast itself (rather than a superscript) also shows up directly as a binary symbol in some texts as an alternative to \star, and in formal language theory a superscript asterisk denotes the Kleene star, \Sigma^{*}, meaning all finite strings over an alphabet.
Other forms
\astasterisk (∗)^{*}superscript star, e.g. conjugateExamples
$f \star g$convolution of two functions
$z^{*}$the complex conjugate of z
$A^{*}$the adjoint of operator A
$\Sigma^{*}$Kleene star, all finite strings over the alphabet Sigma
Tips and common mistakes
- Use
\starfor a genuine binary operation between two symbols, like ; use a superscript ^{*} when starring a single object, like z^{*}. \starand\astrender as visually different glyphs (a five-pointed star versus a small asterisk); pick whichever matches your source's convention and stay consistent.- For a complex conjugate,
\bar{z}(overline) is more common in pure complex analysis, while z^{*} is more common in physics and linear algebra when working with adjoints. - Kleene star in formal language theory is a superscript asterisk on the alphabet or language symbol,
\Sigma^{*}, not the binary\staroperator.
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What's the difference between \star and \ast in LaTeX?
\star renders as a five-pointed star (⋆), commonly used as a binary operator like convolution; \ast renders as a smaller asterisk (∗), commonly used as a superscript modifier on a single symbol.
How do I write a complex conjugate in LaTeX?
Either z^{*} (a superscript asterisk) or \bar{z} (an overline); both are standard, with \bar{z} more common in complex analysis texts.
What is the LaTeX notation for convolution?
is the usual choice, though some texts use instead; either is acceptable if used consistently.
How do I typeset an adjoint operator?
A^{*}, a superscript asterisk placed on the operator symbol.