The Optimization Problem About Spectral Radius Of Non-negative Matrix Hadamard Product

The theory of matrix is an important branch of algebra, is a basicmathematical tool, and it has an important application in mathematics and manyother fields. Now matrix theory has been widely used in wirelesscommunications, financial statistics, system engineering, optimization theory,simulation and other engineering fields, especially in image encryption anddigital watermarking it combines with Matlab effectively.Optimization theory is also an important branch of mathematics, it study thequestion is about which is the best in many projects and how to find the optimalscheme. For example, in the engineering design how to choose parameters of adesign to make the design not only can meet the requirements of the design butcan reduce the cost. The branch of optimization can provide theoretical basis andsolve method, it is a wide application and strong practicability.This dissertation is mainly put forward a special matrix based on theprevious research, but we find not all non-negative matrix type can achieve themost value by some permutation matrix. When A is the non-negative matrix,the most value of ρ(S(?)A) must exist. If the matrix S achieve the most valueof ρ(S(?)A), the corresponding properties and theorems will be given. We can getthe conclusion when A is a positive matrix, ρ(S(?)A) can achieve the mostvalue by some permutation matrix. If A is a symmetric matrix, combiningweakly regular split, we will get corresponding theorems.