Computation of Outer Inverse of Tensors Based on t-Product

Behera, R and Sahoo, JK and Wei, Y (2024) Computation of Outer Inverse of Tensors Based on t-Product. [Preprint]

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Abstract

Tensor computations play an essential role in various fields of science and engineering, including multiway data analysis. In this study, we established a few basic properties of the range and null space of a tensor by using block circulant matrices and a discrete Fourier matrix. We then discuss the outer inverse of the tensors based on (Formula presented.) -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 (Formula presented.) -QR decomposition based algorithm was developed to compute outer inverses. It is well known that the confidentiality of information transmitted through the virtual world grows exponentially, and color image and video security have become a significant concern when communicating over the internet. As an application, a (Formula presented.) -QR decomposition based algorithm was demonstrated for concealing secret color images and videos. © 2024 John Wiley & Sons Ltd.

Item Type:	Preprint
Publication:	Numerical Linear Algebra with Applications
Publisher:	John Wiley and Sons Ltd
Additional Information:	The copyright for this article belongs to the Publisher.
Department/Centre:	Division of Interdisciplinary Sciences > Computational and Data Sciences
Date Deposited:	04 Dec 2024 18:46
Last Modified:	04 Dec 2024 18:46
URI:	http://eprints.iisc.ac.in/id/eprint/86920

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