Some results on the generalized inverse of tensors and idempotent tensors

2014/12/23 by Lizhu Sun, Sun, Lizhu, Baodong Zheng +5
Mathematics · Computer Science · #Tensor decomposition and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1412.7430

Abstract

Let A be an order t dimension m× n× ⋯ × n tensor over complex field. In this paper, we study some generalized inverses of A, the k-T-idempotent tensors and the idempotent tensors based on the general tensor product. Using the tensor generalized inverse, some solutions of the equation A⋅ x^t-1=b are given, where x and b are dimension n and m vectors, respectively. The generalized inverses of some block tensors, the eigenvalues of k-T-idempotent tensors and idempotent tensors are given. And the relation between the generalized inverses of tensors and the k-T-idempotent tensors is also showed.

Related

• The generalized inverses of tensors via the C-Product
• Further results on generalized inverses of tensors via the Einstein product
• A study on the 1-Γ inverse of tensors via the M-Product
• On the extensions of the GD inverse of tensors via the M-Product
• The generalized inverses of the quaternion tensor via the T-product