Talk:Interior product: Difference between revisions
Cmloegcmluin (talk | contribs) unhyphenate "comma basis" |
Notation again |
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!operations | !operations | ||
!progressive product (AKA wedge product, exterior product) | !progressive product (AKA wedge product, exterior product)<br> | ||
a ∧ b | a ∧ b | ||
!regressive product (AKA vee product) | !regressive product (AKA vee product)<br> | ||
a ∨ b | a ∨ b = <nowiki>*</nowiki>(*a ∧ *b) | ||
<nowiki>*</nowiki>(*a ∧ *b) | !right interior product<br> | ||
!right interior product | a ⨽ b = ∗(∗a ∧ b)<br> | ||
a ⨽ b | |||
∗(∗a ∧ b) | |||
examples given where grade(a) ≥ grade(b) | examples given where grade(a) ≥ grade(b) | ||
!(left) interior product | !(left) interior product<br> | ||
a ⨼ b | a ⨼ b = <nowiki>*</nowiki>(a ∧ *b)<br> | ||
<nowiki>*</nowiki>(a ∧ *b) | |||
examples given where grade(a) < grade(b) | examples given where grade(a) < grade(b) | ||
!symmetrical interior product | !symmetrical interior product<br> | ||
a • b = if grade(a) ≥ grade(b), a ⨽ b; else a ⨼ b | a • b = if grade(a) ≥ grade(b), a ⨽ b; else a ⨼ b | ||
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|(in terms of other two interior products) | |(in terms of other two interior products) | ||
|} | |} | ||
== Notation == | |||
As Cmloegcmluin observes above, the <math>\vee</math> notation is not really standard, and this product is usually written as <math>\alpha \mathbin{\lrcorner} \beta</math>. | |||
That is is 'dual' to the wedge product is too vague (there are at least 3 different notions of duality here). One might say it's the adjoint of the wedge product, as <math>\left\langle \alpha \mathbin{\lrcorner} \gamma , \beta \right\rangle = \left\langle \alpha , \beta \wedge \gamma\right\rangle</math>. | |||
So my suggestion is to just use the standard notation. | |||
– [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 13:04, 19 April 2025 (UTC) | |||