Abstract
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.
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Communicated by Fuad Kittaneh.
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Pakmanesh, M., Afshin, H. Numerical ranges of even-order tensor. Banach J. Math. Anal. 15, 59 (2021). https://doi.org/10.1007/s43037-021-00142-w
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DOI: https://doi.org/10.1007/s43037-021-00142-w