I am trying to generalize an algorithm for the construction of certain functions $f:x\in\mathbb{R}\mapsto f(x)\in\mathbb{R}$ that utilizes Wronskian matrices, to the vector version $\boldsymbol{f}:\boldsymbol{x}\in\mathbb{R}^n\mapsto\boldsymbol{f}(\boldsymbol{x})\in\mathbb{R}^n$ 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 "multivariate" Wronskian matrices