ABSTRACT
This chapter deals with developments in calculus of matrices. In recent times the derivatives of the elements of the matrix in various forms have been defined and suitable applications are provided. The authors intend to include in this chapter these various forms.
Section 7.2 introduces the derivative of a matrix with respect to a scalar. Section 7.3 includes derivative of a vector with respect to a vector. The next section, Section 7.4 consists of derivative of a scalar with respect to matrix. The subsequent Section 7.5 contains derivatives of a matrix with respect to elements of a given matrix and the derivative of the entries of a matrix with respect to a matrix respectively. The differential of a matrix forms the content of Section 7.6. Section7.7 deals with the derivative of a matrix with respect to a matrix and Section 7.8 utilizes Kronecker products to establish some derivative formulas. In Section 7.9 another type of definition of a derivative of a matrix with respect to a matrix is given
