摘要
在张量研究中乘法运算起着重要的作用,而由于张量的复杂性,由定义来计算张量的乘法十分不便.给出一种张量与矩阵相乘的递推算法,并特别将此算法应用于讨论四阶张量的相关运算,从而得到二元四次型的一种合同标准形,并给出二维四阶张量正定性的一个判定定理.
The product plays an important role in the study of tensors.Because of the complexity of tensors,calculations starting from the tensors definition are inconvenient.A recursion algorithm about the product between tensors and matrices is proposed.Especially,this algorithm is applied to discuss the related operation of the fourth-order tensors.Then,a congruent standard form of binary-quartic-form is achieved,so as to provide a judging theorem for the positive of the order four dimension two tensors.
出处
《东华大学学报（自然科学版）》
CAS
CSCD
北大核心
2015年第5期711-717,共7页
Journal of Donghua University(Natural Science)
关键词
张量乘法
张量的正定性
递推算法
tensor product
tensor positive
recursion algorithm
