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

doi:10.1007/s10483-009-0605-1

Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (6): 713-716.doi: https://doi.org/10.1007/s10483-009-0605-1

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

邵玥吕存景

Fracture Mechanics Laboratory, Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, P. R. China

收稿日期:2009-03-30 修回日期:2009-05-07 出版日期:2009-06-01 发布日期:2009-06-01

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

Yue SHAO, Cun-Jing LV

Fracture Mechanics Laboratory, Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, P. R. China

Received:2009-03-30 Revised:2009-05-07 Online:2009-06-01 Published:2009-06-01

摘要/Abstract

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.

关键词: positive semi-definite tensor, second-order tensor, uniqueness, decomposition

Abstract: 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.

Key words: positive semi-definite tensor, second-order tensor, uniqueness, decomposition

中图分类号:

邵玥吕存景. A direct proof of uniqueness of square-root of a positive semi-definite tensor[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(6): 713-716.

Yue SHAO;Cun-Jing LV. A direct proof of uniqueness of square-root of a positive semi-definite tensor[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(6): 713-716.

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

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

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