2023/11/29 by Behera, Ratikanta, Sahoo, Jajati Keshari, Wei, Yimin
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2311.17507
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.