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}} | ||