Vector Spaces

Abstract

As usual, a collection of objects will be called a set. A member of the collection is also called an element of the set. It is useful in practice to use short symbols to denote certain sets. For instance, we denote by R the set of all real numbers, and by C the set of all complex numbers. To say that “x is a real number” or that “x is an element of R” amounts to the same thing. The set of all n-tuples of real numbers will be denoted by R ⁿ. Thus “X is an element of R ⁿ” and “x is an n-tuple of real numbers” mean the same thing. A review of the definition of C and its properties is given an Appendix.