Einstein积下张量Drazin逆在张量微分方程中的应用  

APPLICATIONS OF THE DRAZIN INVERSE OF TENSORS VIA EINSTEIN PRODUCT TO TENSOR DIFFERENTIAL EQUATION

作　　者：刘春萌 孙丽珠[1] 卜长江[1] Liu Chunmeng;Sun Lizhu;Bu Changjiang(College of Mathematical Sciences,Harbin Engineering University,Harbin 150001)

机构地区：[1]哈尔滨工程大学数学科学学院,哈尔滨150001

出　　处：《高等学校计算数学学报》2021年第3期193-198,共6页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(No.11801115,No.12071097,No.12042103);黑龙江省自然科学基金(No.QC2018002).

摘　　要：1引言对于正整数TV,令[N]={1,2,…,N}.N阶张量A=(a_(i_(1))…_(i_(N)))1≤i_(j)≤I_(j)(j∈[N])是一个含有I_(1)I_(2)…I_(N)个元素的高维数组[15]。显然,2阶张量是矩阵.C^(I_(1)×…×I_(N))是全体从I_(1)×…×I_(N)维N阶复张量的集合.In 2016,L.Sun et al defined the Moore-Penrose inverse of tensors with the Einstein product and the authors gave the general solutions and the minimum-norm least-square solution of some tensor equations using the Moore-Penrose inverse of tensors.In 2018,J.Ji and Y.Wei defined the Drazin inverse of tensor via Einstein product.In this paper,some properties of tensor derivatives and integrals under Einstein product are given,and we give the solutions of a tensor differential equation according to the Drazin inverse of tensors.

关 键 词：DRAZIN逆 正整数 微分方程 张量 

分 类 号：O151[理学—数学]