I am having trouble with this question, could anyone give me any tips?
Linear map from basis vectors watch
- Thread Starter
- 10-11-2017 15:52
- 10-11-2017 16:07
The conditions on L already define the whole map implicitly, since linear maps are (uniquely) determined by their action on a basis.
So for existence, just define this map explicitly. That is, define L for any vector in R^p, noting that any such vector can be expressed as a unique linear combination of the basis vectors .
For uniqueness, just suppose that two maps and both satisfy the conditions on L given in the questions and prove that they must be equal at any vector in R^p. Again, remember that any such vector can be expressed as a linear combination of the since the form a basis and so span R^p.