Exterior algebra

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.

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Exterior algebra

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]}

See also

• Basic abstract temperament translation code
• Dave Keenan & Douglas Blumeyer's RTT library in Wolfram Language
• Interior product
• Recoverability
• The dual
• User:Mike Battaglia/Exterior Norm Conjecture Table