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](https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=9022&option_lang=eng), 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