ABSTRACT
In previous chapters, we have worked with vectors and matrices algebraically, combining like mathematical objects, solving equations, and so forth. If we look carefully at the basic properties of vector operations (Theorem 1.1.1) and at the characteristics of matrix algebra (Theorems 3.1.1 and 3.1.2), we notice some striking similarities. We have defined operations of addition and scalar multiplication for both vectors and matrices, and these operations follow rules that are identical, if you ignore the obvious differences between vectors (rows or columns) and matrices (generally rectangular). In Chapter 1, some proofs of results about Rn
(e.g., see Theorem 1.4.1 or Theorem 1.5.1) depend on general algebraic properties and do not make explicit use of the fact that the vectors are n-tuples of real numbers.
