2021/11/04 by Pengfei Huang, Huang, Pengfei, Qingzhi Yang +1 · 1 citation
Computer Science · Mathematics · #15A03 #15A69 #15B48 #15B57 #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2111.03245
openalex publication_date 2021/11/04 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
Conjugate partial-symmetric (CPS) tensor is a generalization of Hermitian\nmatrices. For the CPS tensor decomposition some properties are presented. For\nreal CPS tensors in particular, we note the subtle difference from the complex\ncase of the decomposition. In addition to traditional decompositions in the\nform of the sum of rank-one tensors, we focus on the orthogonal matrix\ndecomposition of CPS tensors, which inherits nice properties from decomposition\nof matrices. It then induces a procedure that reobtain the CPS decomposable\nproperty of CPS tensors. We also discuss the nonnegativity of the quartic\nreal-valued symmetric conjugate form corresponding to fourth-order CPS tensors\nin real and complex cases, and establish its relationship to different positive\nsemidefiniteness based on different decompositions. Finally, we give some\nexamples to illustrate the applications of presented propositions.\n