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Rigid Transformations
Rigid Transformations

PH2011 - Physics 2A - University of St Andrews
PH2011 - Physics 2A - University of St Andrews

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... Working in an inner product space V, pick any vector p. The inner product h p, ui is a BF of p and u, and is therefore also a LF of u. We can think of any fixed vector p together with a specified inner product as defining a linear functional. So we can think of inner products as defining linear func ...
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An Introduction to Linear Algebra

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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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