ABSTRACT

This chapter reviews some basic concepts and results encountered in the study of vector spaces such as the notions of subspace, independence, basis, dimension, inner-product, norm and orthogonality. It focuses on the general properties of linear transformations and matrix decompositions, and finally on various matrix operations and applications. The chapter summarizes the most important linear algebra concepts and results from the viewpoint of their applicability in the fields of signal processing, communications and networking. It provides several excellent references available in the linear algebra literature. A vector space is called finite-dimensional, if it admits a basis consisting of a finite number of vectors. The chapter concludes with that linear algebra represents a very important tool for designing efficient algorithms for signal processing, communications, and networking applications.