Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (1)

Search Parameters:
Keywords = diagonally dominated biquadratic tensors

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
26 pages, 487 KiB  
Article
Biquadratic Tensors: Eigenvalues and Structured Tensors
by Liqun Qi and Chunfeng Cui
Symmetry 2025, 17(7), 1158; https://doi.org/10.3390/sym17071158 - 20 Jul 2025
Cited by 1 | Viewed by 205
Abstract
The covariance tensors in statistics and Riemann curvature tensor in relativity theory are both biquadratic tensors that are weakly symmetric, but not symmetric in general. Motivated by this, in this paper, we consider nonsymmetric biquadratic tensors and extend M-eigenvalues to nonsymmetric biquadratic tensors [...] Read more.
The covariance tensors in statistics and Riemann curvature tensor in relativity theory are both biquadratic tensors that are weakly symmetric, but not symmetric in general. Motivated by this, in this paper, we consider nonsymmetric biquadratic tensors and extend M-eigenvalues to nonsymmetric biquadratic tensors by symmetrizing these tensors. We present a Gershgorin-type theorem for biquadratic tensors, and show that (strictly) diagonally dominated biquadratic tensors are positive semi-definite (definite). We introduce Z-biquadratic tensors, M-biquadratic tensors, strong M-biquadratic tensors, B0-biquadratic tensors, and B-biquadratic tensors. We show that M-biquadratic tensors and symmetric B0-biquadratic tensors are positive semi-definite, and that strong M-biquadratic tensors and symmetric B-biquadratic tensors are positive definite. A Riemannian Limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) method for computing the smallest M-eigenvalue of a general biquadratic tensor is presented. Numerical results are reported. Full article
(This article belongs to the Section Mathematics)
Show Figures

Figure 1

Back to TopTop