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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 ...
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This applies to U.S. works where the copyright has expired, often because its first publication occurred prior to January 1, 1929, and if not then due to lack of notice or renewal. See this page for further explanation.
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 ...
Asimov's Guide to the Bible is a work by Isaac Asimov that was first published in two volumes in 1968 and 1969, [1] covering the Old Testament and the New Testament (including the Catholic Old Testament, or deuterocanonical, books (see Catholic Bible) and the Eastern Orthodox Old Testament books, or anagignoskomena, along with the Fourth Book of Ezra), respectively.
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.
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 ...
The components of this bivector are the same as the components of the cross product. The magnitude of this bivector is the square root of the sum of the squares of its components. This shows that the magnitude of the bivector u ∧ v is the area of the parallelogram spanned by the vectors u and v as it lies in the three-dimensional space V. The ...