Some studies in Matrix Theory and applications to generalised clifford algebras and representations of Lie groups
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TextPublication details: 1988Description: iii; 95pSubject(s): Physics | Generalised Clifford Algebra | Lie Groups | Matrix TheoryOnline resources: Click here to access online Dissertation note: 1988Ph.DUniversity of Madras Abstract: Some aspects of Matrix theory and its applications are dealt with in this thesis. "For two matrices A and B of order n x n which satisfy the characteristic equation( x^n) - 1 = 0 , it has been shown that the transformation matrix T (AB) satisfying the relation AT (AB) = T (AB) B, becomes involutional". Clifford and generalised Clifford algebras and their representations, are discussed in this thesis. The theorem on involutional matrices, and Lomont's generalisation, Quantum mechanics of a n-level system, its relationship to Kuryshkin's q-algebras, Finite fourier transform, formation of Hamiltonian of a trunkated harmonic oscillator, indecompasble representations of some Lie algebras,... are some of the concepts discussed and explained in this thesis.
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1988
Ph.D
University of Madras
Some aspects of Matrix theory and its applications are dealt with in this thesis. "For two matrices A and B of order n x n which satisfy the characteristic equation( x^n) - 1 = 0 , it has been shown that the transformation matrix T (AB) satisfying the relation AT (AB) = T (AB) B, becomes involutional". Clifford and generalised Clifford algebras and their representations, are discussed in this thesis. The theorem on involutional matrices, and Lomont's generalisation, Quantum mechanics of a n-level system, its relationship to Kuryshkin's q-algebras, Finite fourier transform, formation of Hamiltonian of a trunkated harmonic oscillator, indecompasble representations of some Lie algebras,... are some of the concepts discussed and explained in this thesis.
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