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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.
For example, in six dimensions with standard basis (e 1, e 2, e 3, e 4, e 5, e 6) the bivector + + is the sum of three simple bivectors but no less. As in four dimensions it is always possible to find orthogonal simple bivectors for this sum.
Now (hr 2) 2 = (−1)(−1) = +1, and the biquaternion curve {exp θ(hr 2) : θ ∈ R} is a unit hyperbola in the plane {x + yr 2 : x, y ∈ R}. The spacetime transformations in the Lorentz group that lead to FitzGerald contractions and time dilation depend on a hyperbolic angle parameter. In the words of Ronald Shaw, "Bivectors are logarithms ...
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]
Since the vector term of the vector bivector product the name dot product is zero when the vector is perpendicular to the plane (bivector), and this vector, bivector "dot product" selects only the components that are in the plane, so in analogy to the vector-vector dot product this name itself is justified by more than the fact this is the non ...
The electromagnetic field at a point p (i.e. an event) of a Lorentzian spacetime is represented by a real bivector F = F ab defined over the tangent space at p. The tangent space at p is isometric as a real inner product space to E 1,3. That is, it has the same notion of vector magnitude and angle as Minkowski spacetime.
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 Blue Letter Bible (BLB) project is an initiative of Sowing Circle, a United States–based, non-denominational Christian ministry that has created a study Bible and Bible study tools stated to "make reading, searching and studying the Bible easy and rewarding". [1] The study Bible and associated resources are provided in CD format, via ...