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This image might not be in the public domain outside of the United States; this especially applies in the countries and areas that do not apply the rule of the shorter term for US works, such as Canada, Mainland China (not Hong Kong or Macao), Germany, Mexico, and Switzerland.
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 ...
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 ...
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.
The torque or curl is then a normal vector field in this 3rd dimension. By contrast, geometric algebra in 2 dimensions defines these as a pseudoscalar field (a bivector), without requiring a 3rd dimension. Similarly, the scalar triple product is ad hoc, and can instead be expressed uniformly using the exterior product and the geometric product.
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 ...
This image might not be in the public domain outside of the United States; this especially applies in the countries and areas that do not apply the rule of the shorter term for US works, such as Canada, Mainland China (not Hong Kong or Macao), Germany, Mexico, and Switzerland.
Isaiah 62 is the sixty-second chapter of the Book of Isaiah in the Hebrew Bible or the Old Testament of the Christian Bible. This book contains the prophecies attributed to the prophet Isaiah, and is one of the Books of the Prophets. [1] Chapters 56-66 are often referred to as Trito-Isaiah. [2]