Linear Algebra- $Tv_j = \sum_{i=1}^{n}v_{i}\otimes w_{ij} $

Question

Let $V$ and $W$ be finite dimensional vector spaces over the same field. Let $T$ be a linear transformation

$T : V \rightarrow V\bigotimes W$.

and $B_V = \{v_1,v_2,...,v_n\}$ is a basis of $V$ and $w_{ij}\in W$ are defined by $Tv_j = \sum_{i=1}^{n}v_{i}\otimes w_{ij} $ show that $\sum_{i=1}^{n}w_{ii}$ is independent of basis of V.

Any Help Please.