In this paper, the numerical range of an even-order tensor is defined using the norm of its square matrix unfolding. The basic properties of the numerical range of a matrix, such as compactness and convexity, are proved to hold for the numerical range of an even-order tensor. Also, we introduce normal tensors based on the contraction product. According to the Tucker decomposition, we get the numerical range of a normal tensor. Next, we introduce the singular-value decomposition (SVD) of an even-order tensor. Using this decomposition, we obtain the numerical range of such a tensor.

中文翻译：

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偶数阶张量的数值范围

在本文中，偶数阶张量的数值范围是使用其方阵展开的范数来定义的。矩阵的数值范围的基本性质，例如紧性和凸性，被证明适用于偶数阶张量的数值范围。此外，我们引入了基于收缩积的法向张量。根据 Tucker 分解，我们得到一个正常张量的数值范围。接下来，我们介绍偶数阶张量的奇异值分解 (SVD)。使用这种分解，我们获得了这种张量的数值范围。