We study the extent to which several classical results relating linear or multilinear forms and their zero-sets can be generalised to linear or bilinear operators with values in \({\mathbb {R}}^n\). We find some analogues of the classical theorems, and also some restrictions.

中文翻译：

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线性和双线性算子及其零集

我们研究了有关线性或多线性形式及其零集的几个经典结果可以推广到\（{\ mathbb {R}} ^ n \）中的线性或双线性算子的程度。我们找到了经典定理的一些类似物，也发现了一些限制。