06-240/Classnotes For Tuesday September 26

Vector Space Examples

1. {0} is vector space over any fields.
2. [math]\displaystyle{ F^n=(a_1,...,a_n), a_i \in F }[/math] and can be represented by
3. [math]\displaystyle{ M_{m \times n}(F)= \left\{\left( \begin{array}{ccc} a_{11}& ... &a_{1n}\\ \vdots & \vdots & \vdots \\ a_{m1} & ... & a_{mn} \end{array} \right) \right\} }[/math]