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

SHAO Yue; LÜ Cun-jing

doi:10.3879/j.issn.1000-0887.2009.06.005

Volume 30 Issue 6

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SHAO Yue, LÜ Cun-jing. Direct Proof of the Uniqueness of the Square-Root of a Positive Semi-Definite Tensor[J]. Applied Mathematics and Mechanics, 2009, 30(6): 663-666. doi: 10.3879/j.issn.1000-0887.2009.06.005

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

doi: 10.3879/j.issn.1000-0887.2009.06.005

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

Received Date: 2009-03-30
Rev Recd Date: 2009-05-08
Publish Date: 2009-06-15

Abstract

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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References

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