Matrix inequalities for the Hadamard product of matrices

The Hadamard product of matrices is widely used in image processing and blind source signal separation and is a hot topic in matrix analysis theory. For nonnegative matrices with nonzero principal diagonal elements, a new upper bound of the spectral radius of the Hadamard product is established by using the eigenvalue inclusion field theorem and a special similar diagonalization operation. The new estimation can be expressed only by the elements of two nonnegative matrices, which is operable and easy to calculate. Finally, an example is given to verify that the estimation formula in this paper is more accurate than that in related research.