Some studies in Matrix Theory and applications to generalised clifford algebras and representations of Lie groups

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.