I am trying to generalize an algorithm for the construction of a certain linear combinations of functions $\boldsymbol{f}:x\in\mathbb{R}\mapsto \boldsymbol{f}(x)\in\mathbb{R}^n$ that utilizes Wronskian matrices, to the multidimensional version $\boldsymbol{f}:\boldsymbol{x}\in\mathbb{R}^m\mapsto\boldsymbol{f}(\boldsymbol{x})\in\mathbb{R}^n$ utilizing "some" multidimensional generalization of Wronskian matrices.

Some online research turned up A. I. Petrov, A multidimensional generalization of the Wronskian, Uspekhi Mat. Nauk, 1964, Volume 19, Issue 5, 194– 196, which is written in Russian language.

Question:is there an English (or German) translation of the above linked paper freely available online?

What else can be recommended as freely accessible resources for the definition of multidimensional Wronskian matrices

**Addendum:**

from the statement "**In the case of functions of several variables, there is no one determinant which may properly be taken as the generalization of the wronskian**" in M. Green's 1916 paper The Linear Dependence of Functions of Several Variables, and Completely Integrable Systems of Homogeneous Linear Partial Differential Equations it became clear that questions about *the* multidimensional Wronskian are ill posed.