Linear operators and positive semidefiniteness of symmetric tensor spaces

DOI10.1007/s11425-014-4930-zzbMath1308.15025OpenAlexW2272070477MaRDI QIDQ2018916

Ziyan Luo, Yinyu Ye, Liqun Qi

Publication date: 26 March 2015

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-014-4930-z

zbMATH Keywords

linear operatorsymmetric tensorSOS conesymmetric positive semidefinite tensor cone

Mathematics Subject Classification ID

Differential geometric aspects in vector and tensor analysis (53A45) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Differential geometry of symmetric spaces (53C35) Multilinear algebra, tensor calculus (15A69)

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Cites Work

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• Tensor Decompositions and Applications
• Approximation algorithms for homogeneous polynomial optimization with quadratic constraints
• Space tensor conic programming
• Semidefinite representation of convex sets
• Perron-Frobenius theorem for nonnegative tensors
• Extension of primal-dual interior point algorithms to symmetric cones
• Eigenvalues of a real supersymmetric tensor
• Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras
• Finding the Largest Eigenvalue of a Nonnegative Tensor
• Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
• Symmetric Tensors and Symmetric Tensor Rank