| 31. | Where'" is the exterior product from exterior algebra or geometric algebra ( in three dimensions the cross product can be used ).
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| 32. | For vectors in "'R "'3, the exterior algebra is closely related to the cross product and triple product.
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| 33. | Equivalently, any two tensors that differ by only an element of the ideal are considered to be the same element in the exterior algebra.
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| 34. | But there is also a functor taking vector spaces to the category of exterior algebras, and a functor taking vector spaces to symmetric algebras.
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| 35. | Then we expect the cohomology ring to be an exterior algebra on a generator of degree two ( the fundamental class ), and indeed,
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| 36. | :I don't really know, but while you're waiting for someone else to come along, try reading Exterior algebra.
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| 37. | Areas are measured with " density " dx \ wedge dy, a differential 2-form which involves the use of exterior algebra.
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| 38. | The associated graded algebra of a Clifford algebra is an exterior algebra; i . e ., a Clifford algebra degenerates to an exterior algebra.
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| 39. | The associated graded algebra of a Clifford algebra is an exterior algebra; i . e ., a Clifford algebra degenerates to an exterior algebra.
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| 40. | From 1880 to 1884, Gibbs worked on developing the exterior algebra of Hermann Grassmann into a vector calculus well-suited to the needs of physicists.
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