摘要: The paper discuss some properties of Kronecker product and Hadamard product of generalized positive definite matrices over the quaternion division ring, and generalize the theorem in [1],[2].关键词: quaternion division ring generalized positive definite matrices Kronecker product Hadamard product ...
A natural Hadamard matrix H n is a 2 n 脳 2 n matrix defined recursively as H n+1= 1 1 1 -1 H n, where denotes the Kronecker product. Some properties of such matrices which follow from the above definition are shown in this paper. These include a certain relation between defined ...
One consider also the approximate l p-inverses (1 p ∞) of the matrices having the block form [ I n A, B T I m], where denotes the Kronecker product, m = r + 1, n = s + 1, I n is the identity matrix of order n, A ∈ R m× r, B ∈ R s× n, rank( A) = r,...
denotes the Kronecker product and is the transposition-permutation matrix associated to (see thereview of matrix algebrabelow for a definition). Proof There is a simpler expression for the covariances between the diagonal entries of : Proof Review of matrix algebra This section reviews some results ...
the authors discussed some important properties of Hada-mard product and Kronecker product of some kinds of generalized positivedefinite matrices.Some necessary and sufficient conditions have been givenfor an nth order real matrix to be generalized positive definite matrice.Theyare generalizetion of ...
It also generalizes the unpenalized ML flip-flop (FF) algorithm of Dutilleul ["The MLE algorithm for the matrix normal distribution," J. Statist. Comput. Simul., vol. 64, pp. 105-123, 1999] and Werner ["On estimation of covariance matrices with Kronecker product structure," IEEE Trans....
This power is an analogue of the representation of the Sylvester-Hadamard matrix in the form of a Kronecker power of H . The properties of the new tensor product of matrices are examined and compared with those of the Kronecker product. An algebraic structure with the matrix H used as a ...
The group was obtained by apply Kronecker product on the demonstration of the quaternion group is a finite group with 32 order. The elements of this group are 4脳4 matrices and the group is a non-abelian. In the first results, it's presented that the group was a solvable group. In ...
We define a generalized Kronecker product for block matrices, mention some of its properties, and apply it to the study of a block Hadamard product of posi... M Günther,L Klotz - 《Linear Algebra & Its Applications》 被引量: 19发表: 2012年 Some statistical properties of Hadamard products ...
Kronecker product (sum)Hadamard productTracy-singh productKhatri-rao productPositive (semi) definite matrixIn the present paper, we give some notes and counterexamples to show that the positive (semi) definite property of the Khatri-Rao and Tracy-Singh products of partitioned matrices are in ...