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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 it questions about the multidimensional Wronskian are ill posed.

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.

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 it questions about the multidmensional Wronskian are ill posed.

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 it questions about the multidimensional Wronskian are ill posed.