Books by T Tamizh Chelvam

Matrices play a vital role in modeling because of the rich techniques available in the domain of matrices. In this aspect, role of the inverse of a matrix is very important and is the fundamental for solution techniques. For a given matrix, the Moore-Penrose inverse is the unique matrix satisfying four fundamental matrix equations. The concept of unitary matrices for non-singular category has been extended as partial isometry to rectangular matrices, via the tool of Moore-Penrose inverses. This beginning has subsequently extended the concept of partial isometry to star-dagger matrices, which coincides with normal matrices in the case of non-singular matrices. The class of hermitian positive semi-definite matrices is a subclass of hermitian matrices, which in turn a subclass of normal matrices. The class of normal matrices includes skew-hermitian, hermitian and unitary matrices. Also another generalization of hermitian matrices is the range-hermitian matrices called the class of EP matrices.

For the last thirty years, due to the involvement in areas such as computer science, electrical and computer engineering and operations research, graph theory has grown exponentially. Study of domination is one of the important sub-areas of graph theory and seen enormous growth due to its varied applications. The study on domination not only restricted to domination parameters, but also relates to the other parameters like independence number, covering number and others. This book deals with certain new domination parameters and their properties with other existing parameters of graphs.