An analog of Hölder's inequality for the spectral radius of Hadamard products

Handle URI:
http://hdl.handle.net/10754/626465
Title:
An analog of Hölder's inequality for the spectral radius of Hadamard products
Authors:
Li, Muxingzi
Abstract:
We prove new inequalities related to the spectral radius ρ of Hadamard products (denoted by ◦ ) of complex matrices. Let p, q ∈ [1 , ∞ ] satisfy 1/p + 1/q = 1, we show an analog of Hölder’s inequality on the space of n × n complex matrices ρ ( A ◦ B ) ≤ ρ ( | A |^( ◦ p) ) ^(1/p) ρ ( | B |^( ◦ q) ) ^(1/q)  for all A, B ∈ C n × n , where |·| denotes entry-wise absolute values, and ( · ) ^ (◦ p) represents the entry-wise Hadamard power. We derive a sharper inequality for the special case p = q = 2. Given A, B ∈ C ^(n × n) , for some β ∈ (0 , 1] depending on A and B , ρ ( A ◦ B ) ≤ βρ ( | A ◦ A | ) ^(1/2) ρ ( | B ◦ B | )^ (1/2) . Analysis for another special case p = 1 and q = ∞ is also included.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
arXiv
Issue Date:
3-Dec-2017
ARXIV:
arXiv:1712.00700
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1712.00700v1; http://arxiv.org/pdf/1712.00700v1
Appears in Collections:
Other/General Submission; Other/General Submission; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLi, Muxingzien
dc.date.accessioned2017-12-28T07:32:11Z-
dc.date.available2017-12-28T07:32:11Z-
dc.date.issued2017-12-03en
dc.identifier.urihttp://hdl.handle.net/10754/626465-
dc.description.abstractWe prove new inequalities related to the spectral radius ρ of Hadamard products (denoted by ◦ ) of complex matrices. Let p, q ∈ [1 , ∞ ] satisfy 1/p + 1/q = 1, we show an analog of Hölder’s inequality on the space of n × n complex matrices ρ ( A ◦ B ) ≤ ρ ( | A |^( ◦ p) ) ^(1/p) ρ ( | B |^( ◦ q) ) ^(1/q)  for all A, B ∈ C n × n , where |·| denotes entry-wise absolute values, and ( · ) ^ (◦ p) represents the entry-wise Hadamard power. We derive a sharper inequality for the special case p = q = 2. Given A, B ∈ C ^(n × n) , for some β ∈ (0 , 1] depending on A and B , ρ ( A ◦ B ) ≤ βρ ( | A ◦ A | ) ^(1/2) ρ ( | B ◦ B | )^ (1/2) . Analysis for another special case p = 1 and q = ∞ is also included.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1712.00700v1en
dc.relation.urlhttp://arxiv.org/pdf/1712.00700v1en
dc.rightsArchived with thanks to arXiven
dc.titleAn analog of Hölder's inequality for the spectral radius of Hadamard productsen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.eprint.versionPre-printen
dc.identifier.arxividarXiv:1712.00700en
kaust.authorLi, Muxingzien
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