Linear Algebra pp 1-22 | Cite as

# Vector Spaces

Chapter

## 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.

## Keywords

Linear Combination Vector Space Rational Number Vector Space Versus Zero Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1987