Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/24051
Title: An even order symmetric B tensor is positive definite
Authors: Qi, L 
Song, Y
Keywords: B tensor
M tensor
Partially all one tensor
Positive definiteness
Issue Date: 2014
Publisher: North-Holland
Source: Linear algebra and its applications, 2014, v. 457, p. 303-312 How to cite?
Journal: Linear algebra and its applications 
Abstract: It is easily checkable if a given tensor is a B tensor, or a B0 tensor or not. In this paper, we show that a symmetric B tensor can always be decomposed to the sum of a strictly diagonally dominated symmetric M tensor and several positive multiples of partially all one tensors, and a symmetric B 0 tensor can always be decomposed to the sum of a diagonally dominated symmetric M tensor and several positive multiples of partially all one tensors. When the order is even, this implies that the corresponding B tensor is positive definite, and the corresponding B0 tensor is positive semi-definite. This gives a checkable sufficient condition for positive definite and semi-definite tensors. This approach is different from the approach in the literature for proving a symmetric B matrix is positive definite, as that matrix approach cannot be extended to the tensor case.
URI: http://hdl.handle.net/10397/24051
ISSN: 0024-3795
EISSN: 1873-1856
DOI: 10.1016/j.laa.2014.05.026
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

SCOPUSTM   
Citations

26
Last Week
0
Last month
1
Citations as of Oct 9, 2017

WEB OF SCIENCETM
Citations

26
Last Week
0
Last month
1
Citations as of Oct 17, 2017

Page view(s)

53
Last Week
0
Last month
Checked on Oct 22, 2017

Google ScholarTM

Check

Altmetric



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.