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Parallel plane segments with the same orientation and area corresponding to the same bivector a ∧ b. [1] In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. Considering a scalar as a degree-zero quantity and a vector as a degree-one quantity, a bivector is ...
Author: Orr, James, 1844-1913, ed: Short title: The International standard Bible encyclopedia; Date and time of digitizing: 03:09, 24 November 2009: Software used
A two-vector or bivector [1] is a tensor of type () and it is the dual of a two-form, meaning that it is a linear functional which maps two-forms to the real numbers (or more generally, to scalars). The tensor product of a pair of vectors is a two-vector. Then, any two-form can be expressed as a linear combination of tensor products of pairs of ...
As recently as 2019, the Android version of the app was requiring access to all the user's contact information (their address book) as well as the user's GPS location. [ 13 ] [ 14 ] YouVersion has updated their privacy policies as of April 2, 2022.
The torque or curl is then a normal vector field in this 3rd dimension. By contrast, geometric algebra in 2 dimensions defines these as a pseudoscalar field (a bivector), without requiring a 3rd dimension. Similarly, the scalar triple product is ad hoc, and can instead be expressed uniformly using the exterior product and the geometric product.
A bivector is an element of the antisymmetric tensor product of a tangent space with itself. In geometric algebra, also, a bivector is a grade 2 element (a 2-vector) resulting from the wedge product of two vectors, and so it is geometrically an oriented area, in the same way a vector is an oriented line segment.
The Committee on Bible Translation wanted to build a new version on the heritage of the NIV and, like its predecessor, create a balanced mediating version–one that would fall in-between the most literal translation and the most free; [3] between word-for-word (Formal Equivalence) [3] and thought-for-thought (Dynamic Equivalence). [3]
A 2-blade is a simple bivector. Sums of 2-blades are also bivectors, but not always simple. A 2-blade may be expressed as the wedge product of two vectors a and b: . A 3-blade is a simple trivector, that is, it may be expressed as the wedge product of three vectors a, b, and c: .