I came across the expression $$ (\boldsymbol{e}_i\otimes\boldsymbol{e}_j)\cdot \boldsymbol{e}_k$$
where $\boldsymbol{e}$ are first order Cartesian tensors and $i,j,k=1,2,3$. Now, i'm simply wondering how to interpret this since i'm used to working with the format $$ (\boldsymbol{e}_i\otimes\boldsymbol{e}_j)\boldsymbol{e}_k$$. I'm guessing there's no difference between the two but it still doesn't sit quite right with me. I'm not too familiar with abstract algebra so I interpret the first one as a scalar product between a second order tensor and a first order tensor. The second expression I interpret as a linear transformation where $(\boldsymbol{e}_i\otimes\boldsymbol{e}_j)$ is operating on $\boldsymbol{e}_k$.
Best regards
Bengt