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## Preview

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## Copyright information

© Springer Science+Business Media New York 1987