New Bounds of Eigenvalues of Hadamard Product and Fan Product of Matrices
LI Yan-ya · Journal of Changchun University · 2015
The paper gives the definitions of k Hadamard power for nonnegative matrix and r Fan power for M matrix. For ∑j≠i ak ijuk j=[ρ( A[k])- ak ii]uk i,∑j≠i bk ijvk j= [ρ( B[k])- bk ii]vk i,it uses Cauchy-schwitz inequality( ξ,η)2≤( ξ,ξ)( η,η) to obtain the spectral radius ρ( A°B) of Hadamard product for nonnegative matrices A and B,as well as some new bounds of minimum eigenvalue τ( A* B)of Fan product for M matrices A and B. These results contain the corresponding conclusions that Fang Mao-zhong gives for this kind of problems.