CHARACTERIZING REAL-VALUED MULTIVARIATE COMPLEX POLYNOMIALS AND THEIR SYMMETRIC TENSOR REPRESENTATIONS

doi:10.1137/141002256

CORC > 上海财经大学 > 上海财经大学

	CHARACTERIZING REAL-VALUED MULTIVARIATE COMPLEX POLYNOMIALS AND THEIR SYMMETRIC TENSOR REPRESENTATIONS
	Jiang, Bo 1; Li, Zhening 2; Zhang, Shuzhong 3
刊名	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
	2016
卷号	37 期号:1 页码:381-408
关键词	symmetric complex tensor conjugate complex polynomial tensor eigenvalue tensor eigenvector Banach's theorem
ISSN号	0895-4798
DOI	10.1137/141002256
英文摘要	In this paper we study multivariate polynomial functions in complex variables and their corresponding symmetric tensor representations. The focus is to find conditions under which such complex polynomials always take real values. We introduce the notion of symmetric conjugate forms and general conjugate forms, characterize the conditions for such complex polynomials to be real valued, and present their corresponding tensor representations. New notions of eigenvalues/eigenvectors for complex tensors are introduced, extending similar properties from the Hermitian matrices. Moreover, we study a property of the symmetric tensors, namely, the largest eigenvalue (in the absolute value sense) of a real symmetric tensor is equal to its largest singular value; the result is also known as Banach's theorem. We show that a similar result holds for the complex case as well. Finally, we discuss some applications of the new notion of eigenvalues/eigenvectors for the complex tensors.
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000373633400017
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/1397]
专题	上海财经大学
作者单位	1.Shanghai Univ Finance & Econ, Sch Informat Management & Engn, Res Ctr Management Sci & Data Analyt, Shanghai 200433, Peoples R China; 2.Univ Portsmouth, Dept Math, Portsmouth PO1 3HF, Hants, England; 3.Univ Minnesota, Dept Ind & Syst Engn, Minneapolis, MN 55455 USA
推荐引用方式 GB/T 7714	Jiang, Bo,Li, Zhening,Zhang, Shuzhong. CHARACTERIZING REAL-VALUED MULTIVARIATE COMPLEX POLYNOMIALS AND THEIR SYMMETRIC TENSOR REPRESENTATIONS[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2016,37(1):381-408.
APA	Jiang, Bo,Li, Zhening,&Zhang, Shuzhong.(2016).CHARACTERIZING REAL-VALUED MULTIVARIATE COMPLEX POLYNOMIALS AND THEIR SYMMETRIC TENSOR REPRESENTATIONS.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,37(1),381-408.
MLA	Jiang, Bo,et al."CHARACTERIZING REAL-VALUED MULTIVARIATE COMPLEX POLYNOMIALS AND THEIR SYMMETRIC TENSOR REPRESENTATIONS".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 37.1(2016):381-408.