An extension of the product operator formalism of NMR is introduced, which uses the Hadamard matrix product to describe many simple spin 1/2 relaxation processes. The utility of this formalism is illustrated by deriving NMR gradient-diffusion experiments to simulate several decoherence models of interest in quantum information processing, along with their Lindblad and Kraus representations.

We provide a simple construction for a matrix representation of the Gale transform of a simplotope, the Cartesian product of simplices. The matrix representation is a Kronecker product of matrices representing the Gale transforms of the component simplices. We also show that Hadamard matrices occur as a special case of this construction.

We prove some general theorems which unify results on arithmetic-geometric mean and some other related matrix inequalities. As an application we obtain some results involving Hadamard product of matrices. Mathematics subject classification (2010): 47A30 15A60.

Nomenclature Hadamard product k k2, k kF spectral norm, Frobenius norm 0l m; 0l l m zero matrix, 0l l Il; 1l m l l identity matrix, l m ones matrix

By making use of the Hadamard product, we define a new class of analytic functions of complex order. Coefficient inequalities, sufficient condition and an interesting subordination result are obtained. 2000 Mathematics Subject Classification: 30C45, 30C50.

The product of two free scalar fields on a manifold is shown to be a well defined operator valued distribution on the GNS Hilbert space of a globally Hadamard product state. Viewed as a new field all n-point distributions exist, giving a new example for a Wightman field on a manifold.

X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan’s conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius.

In this paper, we establish a connection between the Hadamard product and the usual matrixmultiplication. In addition, we study some newproperties of the Hadamard product and explore the inverse problem associated with the established connection, which facilitates diverse applications. Furthermore, we propose a matrix-variate generalized Birnbaum–Saunders (GBS) distribution. Three representatio...

X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan’s conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius.