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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 term "Bible" can refer to the Hebrew Bible or the Christian Bible, which contains both the Old and New Testaments. [2]The English word Bible is derived from Koinē Greek: τὰ βιβλία, romanized: ta biblia, meaning "the books" (singular βιβλίον, biblion). [3]
A 1-blade is a vector. Every vector is simple. 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 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 ...
Given a bivector r = r 1 + hr 2, the ellipse for which r 1 and r 2 are a pair of conjugate semi-diameters is called the directional ellipse of the bivector r. [4]: 436 In the standard linear representation of biquaternions as 2 × 2 complex matrices acting on the complex plane with basis {1, h},
Bibliotheca, a five-volume reader's bible. Bibliotheca is a five-volume [1] version of the Bible created by Adam Lewis Greene [2] published in 2016. It was funded in mid 2014 through a thirty-day Kickstarter campaign for which Greene set a goal of $37,000, but the campaign raised over $1.4 million. [3]