# matrices – Computing with a subvector subspace equipped with a prescribed base on finite files

Leave $$U$$ Be a subspace of the vector space of finite dimensions. $$V$$ over a field $$mathbb {k}$$. Leave $$B_V$$ Y $$B_U$$ be fixed bases for $$V$$ Y $$U$$ respectively. Leave $$u in U$$ and we are going to give us $$[u]_V$$, the vector that represents $$u$$ with respect to $$B_V$$.

How do we calculate effectively? $$[u]_U$$ when $$mathbb {k}$$ Is it a finite field, let's say that of two elements?