The block VEC operator and the block tensor unfolding
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Date
2021
Authors
More, Tshepang
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Abstract
The 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)]
Description
A 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, 2021