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As has been suggested in earlier sections much of geometric algebra generalises well into higher dimensions. The geometric algebra for the real space R n is Cl n (R), and the subspace of bivectors is ⋀ 2 R n. The number of simple bivectors needed to form a general bivector rises with the dimension, so for n odd it is (n − 1) / 2, for n even ...
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For Christians, the Old Testament statements are enhanced by multiple verses such as Matthew 10:8, Luke 10:9 and 9:2, and Acts 5:16 that say "heal the sick". Authors Vern and Bonnie Bullough write in The care of the sick: the emergence of modern nursing, that this is seen as an aspect of following Jesus's example, since so much of his public ...
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 ...
Scofield Reference Bible, page 1115. This page includes Scofield's note on John 1:17. The Scofield Bible had several innovative features. Most important, it printed what amounted to a commentary on the biblical text alongside the Bible instead of in a separate volume, the first to do so in English since the Geneva Bible (1560). [2]
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: .
The ungeneralized 3D vector form of the geometric product is: [2] a b = a ⋅ b + a ∧ b {\displaystyle ab=a\cdot b+a\wedge b} that is the sum of the usual dot (inner) product and the outer (exterior) product (this last is closely related to the cross product and will be explained below).
A Dictionary of the Bible (1863), edited by William Smith, title page for the third volume. A Bible dictionary is a reference work containing encyclopedic entries related to the Bible, typically concerning people, places, customs, doctrine and Biblical criticism. Bible dictionaries can be scholarly or popular in tone.