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.
