Generalized Inverses and Products of Special Classes of Matrices

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.