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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 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 it is n / 2. So for four and five dimensions only two simple bivectors are needed but three are required for six and seven dimensions.
The conjugate transpose of this matrix corresponds to −q, so the representation of bivector q is a skew-Hermitian matrix. Ludwik Silberstein studied a complexified electromagnetic field E + hB, where there are three components, each a complex number, known as the Riemann–Silberstein vector. [5] [6]
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.
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.
Whereas in an English only concordance each instance of a word is listed alphabetically without differentiation and in an exhaustive concordance they are listed alphabetically with an identifying number (Strong's Number or GK Number) keyed to a Dictionary Index to identify the original word, in the Analytical Concordance the English words are divided, within the main entry, according to the ...
Matthew 3 is the third chapter of the Gospel of Matthew in the New Testament. It is the first chapter dealing with the ministry of Jesus , with events taking place some three decades after the close of the infancy narrative related in the previous two chapters.
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.