Special products of matrices

In this thesis, Hadamard, Kronecker, Tracy-Singh, Khatri-Rao and bialternate matrix products are studied. Matrix theory plays an important role in many disciplines such as engineering, statistics and control theory, and each of these products offers a wide range of applications in related fields. In this thesis, the definitions, basic properties and interrelationships of these products are discussed in detail. Furthermore, generalized forms of these matrix products, in particular the Khatri-Rao and Tracy-Singh products, are discussed for analyzing complex matrix structures. Bialternate matrix products and their relation with Kronecker product are analyzed. In addition, polynomial and matrix stability of bialternate matrix products and their eigenvalue properties used in control theory applications are analyzed.