We establish new criteria of compatibility for a linear system of equations (equivalent to the Kronecker–Capelli theorem) or inequalities (equivalent to the S. Chernikov theorem) connected with the conditions of existence of linear interpolation polynomials in Euclidean spaces.

中文翻译：

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欧几里得空间中线性方程组和不等式的算子插值和系统

我们为线性方程组（相当于 Kronecker-Capelli 定理）或不等式（相当于 S. Chernikov 定理）建立了新的兼容性标准，这些方程与欧几里德空间中线性插值多项式的存在条件有关。