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Article
Hamilton's Turns for the Lorentz Group
Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by “turns,” which are equivalence classes of ...
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Chapter
Canonical Forms of Positive Definite Matrices under Congruence: Extensions of the Schweinler-Wigner Extremum Principle
It is well known that a N-dimensional real symmetric [complex hermitian] matrix V is congruent to a diagonal matrix modulo an orthogonal [unitary] matrix[1]. That is, V = S✝DS where D is diagonal and S ∈ SO(N) [S
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Chapter
The Two-Dimensional Symplectic and Metaplectic Groups and Their Universal Cover
We give a detailed discussion of the group Sp(2, R), organized in such a way as to lead to explicit constructive descriptions of the metaplectic group Mp(2) and the universal covering group