Some new connections between matrix products for partitioned and non-partitioned matrices

This paper is concerned with a long list of matrix products for partitioned and non-partitioned matrices, including Kronecker, Khatri–Rao of first kind, Hadamard, Tracy–Singh, Khatri–Rao, block Kronecker, block Hadamard,and box products (sums). Our contribution is to gather the most useful connections of the matrix products from various sources and present them in one place. Several new attractive connections are also added to this collection. We give, as an example, two applications in order to show that these connections play a central role in many applications. These applications are: A block diagonal least-squares problem and a generalization of matrix inequalities involving Khatri–Rao products of positive definite matrices.