H-eigenvalues of Hermitian tensors and some applications

2025/08/17 by Chen, Haojie, Yang, Yang
#Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2508.12476

Abstract

We introduce H-eigenvalue for 2m-th order n-dimensional complex tensors. Then we determine several checkable inclusion sets for H-eigenvalues and derive some criterions for the Hermitian positive definiteness (semi-definiteness) of Hermitian and CPS tensors. We also apply the Hermitian tensors to study holomorphic sectional curvature in complex differential geometry and reprove the algebraic part of recent results by Alvarez-Heier-Zheng and Chaturvedi-Heier.

Citations

• Separability of Hermitian Tensors and PSD Decompositions
• Hermitian Tensor Decompositions
• Approximation Algorithms for Optimization of Real-Valued General Conjugate Complex Forms
• A remark on our paper "Negative Holomorphic curvature and positive canonical bundle"
• Quasi-negative holomorphic sectional curvature and positivity of the\n canonical bundle
• An S-type eigenvalue localization set for tensors
• Characterizing Real-Valued Multivariate Complex Polynomials and Their Symmetric Tensor Representations

Related

• Hermitian Tensor Decompositions
• Hermitian tensor and quantum mixed state
• A new S-type eigenvalue localization set for tensors and its applications
• Lower and upper bounds for H-eigenvalues of even order real symmetric tensors
• Hessian comparison and eigenvalue estimate of almost Hermitian manifolds