The term for an operation between two [[Vector|Vectors]] $\vec a, \vec b$, which is equal to the [[Matrix Multiplication|Product]] of: $\huge \begin{align} \let \vec a &\in \R^{n}\\ \let \vec b &\in \R^{m}\\ \\ \vec a \otimes \vec b &= \vec a \vec b^{\intercal} \end{align} $ The [[Trace]] of the [[Outer Product]] between two [[Matrix|Matrices]] $\vec u, \vec v$ is equal to the [[Inner Product]] between $\vec u, \vec v$. $\huge \mathrm{tr}(\vec u \otimes \vec{v}) = \braket{\vec u, \vec v} $ >[!seealso] See Also its 'inverse': [[Inner Product]]