2011 by Taylor & Francis Group, LLC. This chapter will first review 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, and then will focus on the general properties of linear transformations and matrix decompositions (LU, Cholesky, SVD and QR), and finally on various matrix operations and applications. This chapter represents a brief summary of the most important linear algebra concepts and results from the viewpoint of their applicability in the fields of signal processing, communications and networking. In writing this chapter, we made use of several excellent references available in the linear algebra literature [1-8]. For a more detailed description and additional topics, the readers are directed to these excellent references.