广西民族大学学报（自然科学版）2025，Vol.31Issue(1)：73-84,12.
C-乘积下张量广义逆的性质及扰动理论
The Properties and Perturbation Theories of the Generalized Inverse of Tensors Based on the C-Product
摘要
Abstract
In this paper,we mainly study the properties and the perturbation theories of the generalized inverse of tensors under the C-product.Firstly,we introduce the definition and related properties of the C-product,provide some decomposition forms of the tensor generalized inverses,and explore the perturbation theory of the tensor generalized inverses under the C-product.The main results are divided into:using the C-SVD to discuss the perturbation theory of the Moore-Penrose inverse of tensors,using the C-HS decomposition to study the perturbation theory of the core inverse of tensors,and using the C-Schur decomposition to explore the perturbation theory of the core-EP inverse of tensors.关键词
C-乘积/Moore-Penrose逆/core逆/core-EP逆/扰动Key words
C-product/Moore-Penrose inverse/Core inverse/Core-EP inverse/Perturbation分类
数学引用本文复制引用
刘晓冀,王锡媛,靳宏伟..C-乘积下张量广义逆的性质及扰动理论[J].广西民族大学学报（自然科学版）,2025,31(1):73-84,12.基金项目
国家自然科学基金项目(12061015) （12061015）
广西自然科学基金项目(2018GXNSFDA281023) （2018GXNSFDA281023）
广西科技基地与人才专项基金项目(桂科AD21220024). （桂科AD21220024）
