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Chapter 3 Vectors
Chapter 3 Vectors

... Many aspects of physics involve a description of a location in space. In Chapter 2, for example, we saw that the mathematical description of an object’s motion requires a method for describing the object’s position at various times. This description is accomplished with the use of coordinates, and i ...
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Lecture Notes on General Relativity
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... same as those of ηρσ ; that is what it means for the interval to be invariant under these transformations. The matrices which satisfy (1.14) are known as the Lorentz transformations; the set of them forms a group under matrix multiplication, known as the Lorentz group. There is a close analogy betwe ...
Lecture Notes on General Relativity
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... same as those of ηρσ ; that is what it means for the interval to be invariant under these transformations. The matrices which satisfy (1.14) are known as the Lorentz transformations; the set of them forms a group under matrix multiplication, known as the Lorentz group. There is a close analogy betwe ...
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Van Der Vaart, H.R.; (1966)An elementary deprivation of the Jordan normal form with an appendix on linear spaces. A didactical report."
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Four-vector

In the theory of relativity, a four-vector or 4-vector is a vector in Minkowski space, a four-dimensional real vector space. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations, boosts (a change by a constant velocity to another inertial reference frame), and temporal and spatial inversions. Regarded as a homogeneous space, the transformation group of Minkowski space is the Poincaré group, which adds to the Lorentz group the group of translations. The Lorentz group may be represented by 4×4 matrices.The article considers four-vectors in the context of special relativity. Although the concept of four-vectors also extends to general relativity, some of the results stated in this article require modification in general relativity.
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