A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on the representation theory of Brauer algebras. A general procedure for the decomposition of the tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules, together with trace contractions from a Brauer algebra and some mod...

Kronecker products of complex characters of the symmetric group Sn have been studied in many papers. Information on special products and on the coefficients of special constituents have been obtained but there is no efficient combinatorial algorithm in sight for computing these products. In [1], products of Sn-characters with few homogeneous components and homogeneous products of characters of ...

Firstly, two new kinds of Kronecker decompositions is developed, i.e. KPGD and KPID; Secondly, the sufficient and necessary conditions and algorithms of Kronecker product(KPD), KPGD, and KPID are discussed; At last, some useful properties of the rank of the sum of Kronecker product gemel decompositions are obtained.

In this paper we propose a Kronecker-based modeling of large networks with unknown interconnection links. The class of Kronecker networks is defined for which we formulate a Vector Autoregressive model. Its coefficient-matrices are decomposed into a sum of Kronecker products. When the network is labeled such that the number of terms in the sum is small compared to the size of the matrix, exploi...

State based analysis of stochasticmodels for performance and dependability often requires the computation of the stationary distribution of a multidimensional continuous-time Markov chain (CTMC). The infinitesimal generator underlying a multidimensional CTMC with a large reachable state space can be represented compactly in the form of a block matrix in which each nonzero block is expressed as ...

The infinitesimal generator matrix underlying a multidimensional Markov chain can be represented compactly by using sums of Kronecker products of small rectangular matrices. For such compact representations, analysis methods based on vector-Kronecker product multiplication need to be employed. When the factors in the Kronecker product terms are relatively dense, vectorKronecker product multipli...

In this paper, we give upper and lower bounds for the spectral norms of circulant matrices A n = Circ(F n−1) and B n = Circ(L (k,h) n and L (k,h) n are the (k, h)-Fibonacci and (k, h)-Lucas numbers, then we obtain some bounds for the spectral norms of Kronecker and Hadamard products of these matrices.

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.

We consider association schemes with d classes and the underlying BoseMesner algebra, A . Then, by taking into account the relationship between the Hadamard and the Kronecker products of matrices and making use of some matrix techniques over the idempotents of the unique basis of minimal orthogonal idempotents of A , we prove some results over the Krein parameters of an association scheme.