1.3 Matrix Arithmetic
In this section, we introduce the standard notations used for matrices and vectors and define arithmetic operations (addition, subtraction, and multiplication) with matrices. We will also introduce two additional operations: scalar multiplication and transposition. We will see how to represent linear systems as equations involving matrices and vectors and then derive a theorem characterizing when a linear system is consistent.
The entries of a matrix are called scalars. They are usually either real or complex numbers. For the most part, we will be working with matrices whose entries are real numbers. Throughout the first five chapters of the book, the reader may assume that the term scalar refers to a real number. However, ...
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