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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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.

作者邵玥吕存景

机构地区 Fracture Mechanics Laboratory

出处《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第6期713-716,共4页 应用数学和力学（英文版）

关键词 positive semi-definite tensor second-order tensor UNIQUENESS decomposi-tion positive semi-definite tensor, second-order tensor, uniqueness, decomposi-tion

分类号 O302 [理学—力学]

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Applied Mathematics and Mechanics(English Edition)

2009年第6期

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

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