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arXiv · 2311.17507

Computation of outer inverse of tensors based on $t$-product

Ratikanta Behera·Jajati Keshari Sahoo·Yimin Wei
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Abstract

Tensor operations play an essential role in various fields of science and engineering, including multiway data analysis. In this study, we establish a few basic properties of the range and null space of a tensor using block circulant matrices and the discrete Fourier matrix. We then discuss the outer inverse of tensors based on $t$-product with a prescribed range and kernel of third-order tensors. We address the relation of this outer inverse with other generalized inverses, such as the Moore-Penrose inverse, group inverse, and Drazin inverse. In addition, we present a few algorithms for computing the outer inverses of the tensors. In particular, a $t$-QR decomposition based algorithm is developed for computing the outer inverses.

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Ratikanta Behera, Jajati Keshari Sahoo, Yimin Wei. 2023-11-29. Computation of outer inverse of tensors based on $t$-product. https://arxiv.org/abs/2311.17507

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