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Uncommon card · Science
Exterior algebra, an Uncommon card
In mathematics, the exterior algebra or Grassmann algebra of a vector space V is an associative algebra that contains V, which has a product, called exterior product or wedge product and denoted with ∧, such that v ∧ v = 0 for every vector v in V.
- Rarity
- Uncommon
- Domain
- Science
- ATK
- 82
- DEF
- 66
- Power
- 148
- Wikipedia reads a year
- 100,000
Power 148 (ATK + DEF): stronger than 75 % of WikiCards cards.
The facts on the card
The card carries these facts from its Wikipedia article.
- The wedge product was introduced originally as an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues: the magnitude of a 2-blade v ∧ w is the area of the parallelogram defined by v and w, and, more generally, the magnitude of a k -blade is thevolume of the parallelotope defined by the constituent vectors.
- Its bilinearity, expected from such a generalization of volume, and its alternating property that v ∧ v = 0 implies a skew-symmetric property that v ∧ w = − w ∧ v, and more generally any blade flips sign whenever two of its constituent vectors are exchanged, corresponding to a parallelotope of opposite orientation.
- The full exterior algebra contains objects that are not themselves blades, but linear combinations of blades, a sum of blades of homogeneous degree k is called a k-vector, while a more general sum of blades of arbitrary degree is called a multivector.
Why it is Uncommon
Rarity in WikiCards follows a year of Wikipedia page views: the most read articles become Epic and Legendary cards. The Exterior algebra article was read about 100,000 times in a year. ATK comes from the length of the article and DEF from its quality, so this card hits with 82 and blocks with 66: each hit it takes is cut by 26 %.
How to get Exterior algebra
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Credits
Text : Wikipedia, Exterior algebra (revision), CC BY-SA 4.0. Photo : Maschen, CC0, Wikimedia Commons.





