Let A=[aij] be an n-by-n complex matrix A, its numerical radius is w(A)=max{|<Ax,x>|∈C∶x∈C^n, ||x||=1}. Let B=[bij] be an m-by-m complex matrix, the tensor product A ⊗B of A and B is the (mn)-by-(mn) matrix [aijB]. If m=n, then the Hadamard product A○B of A and B is the n-by-n matrix [aijbij]. The main concern of this project is the relations between the numerical radius of A⊗B (resp., A○B) and those of $A$ and $B$. For one direction, we have the following inequality.) and those of $A$ and $B$. For one direction, we have the following inequality:w(A○B)≤w(A⊗B)≤||A||w(B).In this project, we want to obtain necessary and sufficient conditions for the equality w(A⊗B)=||A||w(B) (resp., w(A○B)=||A||w(B)) to hold. For each inequality, we have given theconjecture for the equality to hold, we will prove these conjectures as the purpose of this project.
Status | Finished |
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Effective start/end date | 1/08/20 → 31/07/21 |
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In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This project contributes towards the following SDG(s):