A direct proof of uniqueness of square-root of a positive semi-definite tensor  

作　　者：邵玥 吕存景 

机构地区：[1]Fracture Mechanics Laboratory,Department of Engineering Mechanics,School of Aerospace,Tsinghua University,Beijing 100084,P. R. China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2009年第6期713-716,共4页应用数学和力学（英文版）

摘　　要：Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without resorting to the notion of eigenvalues, eigenvectors and the spectral decomposition of the second-order symmetric tensor.Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without resorting to the notion of eigenvalues, eigenvectors and the spectral decomposition of the second-order symmetric tensor.

关 键 词：positive semi-definite tensor second-order tensor UNIQUENESS decomposi-tion 

分 类 号：O302[理学—力学]