Article ID Journal Published Year Pages File Type
8897689 Linear Algebra and its Applications 2018 9 Pages PDF
Abstract
Let A and B be nonnegative square matrices of the same order. Denote by ‖⋅‖ and ρ(⋅) the spectral norm and the spectral radius respectively. We prove the following inequalities:‖A∘B‖≤‖A∘A‖12‖B∘B‖12;‖A∘B‖≤ρ12(ATB∘BTA)≤ρ12(ATB∘ATB)≤ρ(ATB), where ∘ denotes the Hadamard product. This interpolates the inequality‖A∘B‖≤ρ(ATB) due to Huang. Some spectral norm inequalities for an arbitrarily finite number of nonnegative square matrices are also obtained, which refine some other results of Huang.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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