More, Tshepang2021-12-192021-12-192021https://hdl.handle.net/10539/32468A dissertation submitted in fulfilment of the requirements for the degree of Master of Science to the Faculty of Science, School of Mathematics, University of the Witwatersrand, Johannesburg, 2021The Kronecker product is the unique bilinear product of matrices which arises from vectorization via the vec operator and matrix multiplication. This ap proach may be generalized to the block vec operator and the block Kronecker product which are defined for arbitrary partitioned block matrices. This disser tation brings to light a novel approach of describing balanced and unbalanced partitioned block matrices and discusses properties of the block vec operator and the block Kronecker product. This novel approach is extended to block tensors and block tensor unfoldings following the work in [Lin. Alg. Appl. 149,165-184(1991)] and [SIAM J. Matrix Anal. Appl. 33(1),149-169 (2012)]enThesis