Mathematical objects are supposed to "model things", sometimes, more mathematics. In this sense, i think is "natural" to assume that tensors, being such universal objects as they are, should serve to model simpler things, as arithmetic operations... then again maybe i'm mistaken. After studying a little bit about tensors, i haven't seen anything that relates them to ordinary arithmetics, despite the obvious analogy. Talking more concretely, if i have a field $\mathbb{F}$ with elements $a,b,c,d\in \mathbb{F}$, they will show to equate to a value $K$ in the following manner: $$K=(a+b)(c+d)$$ $$=ac+ad+bc+bd$$ Also the Kronecker product between the vectors $\vec{v}=(a;b)$ and $\vec{w}=(c;d)$ is a matrix $M$ that shows: $$M=\vec{v}\otimes \vec{w}= \begin{bmatrix} ac & ad \\ bc & bd \end{bmatrix}$$ The objects $M$ and $K$ are evidently similar, so, my question is: are they related by some mathematical formalism? If so, wich one? Is there a mapping $f$ that shows $f(M)=K$?
S.N.: I might have messed up the ordering or shape of the entries of the Kronecker product, please do not fixate your attention on that.
After talking a little bit with some friends, we came to the conclussion that there is an obvious multilinear form $\gamma:\mathbb{F}^2\otimes\mathbb{F}^2\rightarrow \mathbb{F}$ that maps $M\mapsto K$, given by $$\gamma(A)=\sum_{(i,j)\in I^2} A^{ij}$$ Where $I^2$ is the index set of the matrix $A$, and $A^{ij}$ is the entry of $A$ corresponding to the i-th column and the j-th row. Thus, it is clear that: $$\gamma(M)=\sum_{(i,j)\in I^2} M^{ij}=ac+ ad +bc +bd$$