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The geometric algebra is Cl 3,1 (R), and the subspace of bivectors is ⋀ 2 R 3,1. The simple bivectors are of two types. The simple bivectors e 23, e 31 and e 12 have negative squares and span the bivectors of the three-dimensional subspace corresponding to Euclidean space, R 3. These bivectors generate ordinary rotations in R 3.
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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 ...
The fundamental difference is that GA provides a new product of vectors called the "geometric product". Elements of GA are graded multivectors: scalars are grade 0, usual vectors are grade 1, bivectors are grade 2 and the highest grade (3 in the 3D case) is traditionally called the pseudoscalar and designated .
The chapter begins with God giving Moses a message for the Israelites about the need to be holy, to respect parents, and to avoid idolatry (verses 1–4). Next are instructions for peace offerings (5-8), food aid for poor people and foreigners (9-10), and various instructions relating to ethical treatment of others (11-18) and agricultural ...
Noteworthy translation aspects in this verse are the name of Adam's wife, the future tense "will conceive" mixed with the past tense "knew", "said" and "obtained", the lack of quote marks, and translation of the Tetragrammaton. The Divine Name, Jehovah, is featured prominently throughout the Old Testament of this Bible version.
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
The New International Version (NIV) is a translation of the Bible into contemporary English. Published by Biblica , the complete NIV was released on October 27, 1978 [ 6 ] with a minor revision in 1984 and a major revision in 2011.