spezielles Tensorprodukt, die Abbildung \begin{eqnarray}\begin{array}{l}\otimes :({V}_{1}^{*}\otimes \cdots \otimes {V}_{m}^{*})\times ({U}_{1}^{*}\otimes \cdots \otimes {U}_{n}^{*})\\\quad \to {V}_{1}^{*}\otimes \cdots \otimes {V}_{m}^{*}\otimes {U}_{1}^{*}\otimes \cdots \otimes {U}_{n}^{*},\\ \qquad (f,g)\mapsto f\otimes g,\end{array}\end{eqnarray}

definiert durch \begin{eqnarray}\begin{array}{l}f\otimes g:{V}_{1}\times \cdots \times {V}_{m}\times {U}_{1}\times \cdots \times {U}_{n}\to {\mathbb{R}};\\ \quad ({\upsilon}_{1},\ldots, {\upsilon}_{m},{u}_{1},\ldots, {u}_{n})\mapsto \\ \qquad f({\upsilon}_{1},\ldots, {\upsilon}_{m})\cdot g({u}_{1},\ldots, {u}_{n}).\end{array}\end{eqnarray}

Hierbei sind V₁,…,V_m, U₁,…,U_n endlichdimen-sionale reelle Vektorräume, und W^∗ ist der Dualraum zum Vektorraum W.