Properties of positive definite matrices and applications

The purpose of this paper is to investigate the properties of positive definite matrices, and in some cases positive semidefinite matrices, and their applications.

Chapter 1 introduces some general properties of positive definite matrices. Chapter 2 investigates how positive definite and positive semidefinite matrices are characterized in terms of positive definiteness and semidefiniteness on arbitrary closed convex cones in the real n-tuple space.

Chapter 3 is concerned with Hadamard products of positive definite matrices, and Kronecker product of positive definite and positive semidefinite matrices.

Chapter 4 discusses some applications of positive definite matrices in vibrating bodies, transformation of axes, convex functions and quadratic programming.