Author(s)

Zhou Ping, Li Yaotang, Gao Meiping

Corresponding Author

Zhou Ping

ABSTRACT

Estimation of matrix eigenvalues is one of the important problems in matrix theory. In this paper, the upper bound of the maximum eigenvalue of Hadamard product of a nonnegative matrix is estimated by using the method of estimating the eigenvalue of a matrix in an elliptic region. By using the maximum value of the sum of rows of matrix elements except principal diagonal elements, the lower bounds of the minimum eigenvalues of the Hadamard product of a matrix, an inverse matrix and two matrices are estimated. In this paper, new estimators of the minimum eigenvalue lower bound of the inverse matrix of a nonsingular matrix and the Hadamard product of a matrix are given. These estimators only depend on the elements of the matrix. Due to the deep research of non-negative matrices, the study of non-negative matrix Hadamard products has also been broadened. The estimation of the upper bound of the maximum eigenvalue of the matrix Hadamard product has been successively obtained many results, which depend on the maximum eigenvalue and the main diagonal element of the two non-negative matrices. The matrix Hadamard product determinant inequality has obtained the results of some semi-positive definite matrix Hadamard product determinant inequalities and the results of some matrix Hadamard product determinant inequalities.

KEYWORDS

Matrix eigenvalue, Hadamard product, Inverse matrix