Open Access

Doaa Al-Saafin

• The Hadamard product of two matrices of the same order is obtained by entry-wise multiplication of their coefficients. In a similar way, the Hadamard power of a matrix and a polynomial is formed by real powers of their coefficients. Results for the Hadamard product of some important classes of matrices, e.g., positive definite matrices, conditionally negative definite matrices, and matrices with one positive eigenvalue are presented. The results are extended to give sufficient conditions for symmetric matrices to have exactly one positive eigenvalue. A Hurwitz (or stable) polynomial is a real polynomial whose roots are located in the open left half of the complex plane. Results for the Hadamard square root of Hurwitz polynomials of degree five are given. Also, a type of Oppenheim's inequality for Hurwitz matrices is presented. Finally, interval matrices, i.e., matrices with intervals as entries are studied, and new results for the interval property of several classes of matrices, e.g., inverse M-matrices, conditionally positive (negative) semidefinite matrices, and infinitely divisible matrices are given.