We investigate the Hadamard product of inverse M-matrices and present two classes of inverse M-matrices that are closed under the Hadamard multiplication. In the end, we give some inequalities on the Fan product of M-matrices and Schur complements. © 2000 Elsevier Science Inc. All rights reserved. AMS classification: 15A09; 15A42

The Hurwitz stable polynomials are important in the study of differential equations systems and control theory (see [7] and [19]). A property of these polynomials is related to Hadamard product. Consider two polynomials p, q ∈ R[x]: p(x) = anx n + an−1x n−1 + · · ·+ a1x + a0 q(x) = bmx m + bm−1x m−1 + · · ·+ b1x + b0 the Hadamard product (p ∗ q) is defined as (p ∗ q)(x) = akbkx + ak−1bk−1x + · ...

In this paper we introduce operator preinvex functions and establish a Hermite–Hadamard type inequality for such functions. We give an estimate of the right hand side of a Hermite–Hadamard type inequality in which some operator preinvex functions of selfadjoint operators in Hilbert spaces are involved. Also some Hermite–Hadamard type inequalities for the product of two operator preinvex functio...

In 1867, Syvlester noted that the Kronecker product of two Hadamard matrices is an Hadamard matrix. This gave a way to obtain an Hadamard matrix of exponent four from two of exponent two. Early last decade, Agayan and Sarukhanyan found a way to combine two Hadamard matrices of exponent two to obtain one of exponent three, and just last year Craigen, Seberry and Zhang discovered how to combine f...

Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in ...

Under the entrywise dominance partial ordering, T.L. Markham and R.L. Smith obtained a Schur complement inequality for the Hadamard product of two tridiagonal totally nonnegative matrices. Applying the properties of the Hadamard core of totally nonnegative matrices, the Schur complement inequalities for the Hadamard product of totally nonnegative matrices is obtained, which extends those of T.L...

Under the entrywise dominance partial ordering, T.L. Markham and R.L. Smith obtained a Schur complement inequality for the Hadamard product of two tridiagonal totally nonnegative matrices. Applying the properties of the Hadamard core of totally nonnegative matrices, the Schur complement inequalities for the Hadamard product of totally nonnegative matrices is obtained, which extends those of T.L...

We apply support vector learning to attributed graphs where the kernel matrices are based on approximations of the Schur-Hadamard inner product. The evaluation of the Schur-Hadamard inner product for a pair of graphs requires the determination of an optimal match between their nodes and edges. It is therefore efficiently approximated by means of recurrent neural networks. The optimal mapping in...

In this paper, some inequalities Hadamard-type for (h, r)-convex functions are given. Furthermore, we also proved some Hadamard-type inequalities for product of two (h, r)-convex functions. Mathematics Subject Classification: 26D15