ABSTRACT
This chapter is of a preliminary character. Here we accumulate results about finite matrices. In particular, we present various inequalities for the eigenvalues and singular values of matrices. In addition, we discuss estimates for the resolvents and determinants of finite matrices, as well as variations of eigenvalues under perturbations. The chapter also contains the well-known inequalities for convex functions. The material of this chapter is systematically used in the proofs of the results presented in the remaining chapters of the book.
