14-240/Tutorial-November11

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Boris

Coordinate and Matrix Representation Problems

Recall:

Let [math]\displaystyle{ V }[/math] be a finite dimensional vector space over a field [math]\displaystyle{ F }[/math]. Let [math]\displaystyle{ B = {v_1, v_2, v_3, ..., v_n} }[/math] be an ordered basis of [math]\displaystyle{ V }[/math] and [math]\displaystyle{ v \in V }[/math]. Then [math]\displaystyle{ v = \displaystyle\sum_{i=1}^{n} c_iv_i }[/math] where [math]\displaystyle{ c_i \in F }[/math]. Then the coordinate representation of [math]\displaystyle{ V }[/math] is defined by [math]\displaystyle{ [v]_B = [c_1, c_2, c_3, ..., c_n] }[/math].