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.

Let’s setup one useful form of tensor notation, which incorporates the matrix and inner product, the outer product, the Hadamard (MATLAB .* or ◦) product diag and diag−1. These will be denoted using different combinations of pairs of up-stairs and down-stairs indices. If we have only 2 order tensors (and lower) we want to be able to easily convert the result into matrix representation. We have ...

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...

Very recently N.E.Cho, O.S.Kwon and H.M.Srivastava (J.Math. Anal. Appl. 292(2004), 470-483) have introduced and investigated a special linear operator I λ p (a, c) defined by the Haramard product (or convolution). In this paper we consider some inclusion properties of a class B p (a, c, α;h) of multivalent analytic functions associated with the operator I λ p (a, c). We have made use of differe...

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.

This survey paper contains recent results for power matrix means and related inequalities for convex functions, Hadamard product of matrices as well as some inequalities involving exponential function of matrices.

A major application of the FFT is fast convolution or fast ltering where the DFT of the signal is multiplied term-by-term by the DFT of the impulse (helps to be doing nite impulse response (FIR) ltering) and the time-domain output is obtained by taking the inverse DFT of that product. What is less well-known is the DFT can be calculated by convolution. There are several di erent approaches to t...