半正定张量半正定方根唯一性的直接证明

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Direct Proof of the Uniqueness of the Square-Root of a Positive Semi-Definite Tensor

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

摘要: 研究半正定张量半正定方根的唯一性问题．避开了二阶张量特征值的概念和对称二阶张量谱分解定理，运用简单的预备知识，直接证明了二阶半正定张量半正定方根的唯一性．
- 半正定 /
- 二阶张量 /
- 唯一性 /
- 分解
Abstract: Understanding the basic properties of the positive semi-definite tensor is prerequisite for its wide application in theoretical and practical field,especially for its square-root.The uniqueness of the square-root of a positive semi-definite tensor was proven without resorting to the notion of eigenvalues,eigenvectors and the spectral decomposition of the second-order symmetric tensor.
- positive semi-definite tensor /
- second-order tensor /
- uniqueness /
- decomposition

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