Exterior algebra: Difference between revisions
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'''Exterior algebra''' is a type of {{w|Algebra over a field|algebra}} which has a product, called '''exterior product''' or '''wedge product''' and denoted with <math>\wedge</math>, such that <math>v \wedge v = 0</math> for every vector <math>v</math> in the vector space <math>V</math>. | '''Exterior algebra''' is a type of {{w|Algebra over a field|algebra}} which has a product, called '''exterior product''' or '''wedge product''' and denoted with <math>\wedge</math>, such that <math>v \wedge v = 0</math> for every vector <math>v</math> in the vector space <math>V</math>. | ||
In [[regular temperament theory]], exterior algebra is typically applied to the vector space of [[val]]s (or maps). The exterior product of two or more vals is called a | In [[regular temperament theory]], exterior algebra is typically applied to the vector space of [[val]]s (or maps). The exterior product of two or more vals is called a multival, and its canonical form is called a [[wedgie]] (or [[Plücker coordinates]]), which can be used to uniquely identify a regular temperament. | ||
Nowadays, most theorists prefer avoiding the exterior algebra approach, since it tends to be overcomplicated with little to no extra benefit.{{clarify}} | Nowadays, most theorists prefer avoiding the exterior algebra approach, since it tends to be overcomplicated with little to no extra benefit.{{clarify}} | ||
Revision as of 06:01, 27 December 2024
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This is a beginner page. It is written to allow new readers to learn about the basics of the topic easily. The corresponding expert page for this topic is Dave Keenan & Douglas Blumeyer's guide to EA for RTT. |
Exterior algebra is a type of algebra which has a product, called exterior product or wedge product and denoted with [math]\displaystyle{ \wedge }[/math], such that [math]\displaystyle{ v \wedge v = 0 }[/math] for every vector [math]\displaystyle{ v }[/math] in the vector space [math]\displaystyle{ V }[/math].
In regular temperament theory, exterior algebra is typically applied to the vector space of vals (or maps). The exterior product of two or more vals is called a multival, and its canonical form is called a wedgie (or Plücker coordinates), which can be used to uniquely identify a regular temperament.
Nowadays, most theorists prefer avoiding the exterior algebra approach, since it tends to be overcomplicated with little to no extra benefit.[clarification needed]