منابع مشابه
Kronecker Products and BIBDs
Recursive constructions are given which permit, under conditions described in the paper, a (v, b, r, k, lambda)configuration to be used to obtain a (v', b', r', k, lambda)-configuration. Although there are many equivalent definitions we will mean by a (v, b, r, k, lambda)-configuration or BIBD that (0, 1)-matrix A of size v x b with row sum r and column sum k satisfying AAT = (r lambda)I + lamb...
متن کاملUnimodality via Kronecker Products
We present new proofs and generalizations of unimodality of the q-binomial coefficients ( n k ) q as polynomials in q. We use an algebraic approach by interpreting the differences between numbers of certain partitions as Kronecker coefficients of representations of Sn. Other applications of this approach include strict unimodality of the diagonal q-binomial coefficients and unimodality of certa...
متن کاملSymmetric Kronecker Products and Semiclassical Wave Packets
We investigate the iterated Kronecker product of a square matrix with itself and prove an invariance property for symmetric subspaces. This motivates the definition of an iterated symmetric Kronecker product and the derivation of an explicit formula for its action on vectors. We apply our result for describing a linear change in the matrix parametrization of semiclassical wave packets.
متن کاملOn the Kronecker Products and Their Applications
This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vecpermutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of...
متن کاملOn Kronecker products, tensor products and matrix differential calculus
The algebra of the Kronecker products of matrices is recapitulated using a notation that reveals the tensor structures of the matrices. It is claimed that many of the difficulties that are encountered in working with the algebra can be alleviated by paying close attention to the indices that are concealed beneath the conventional matrix notation. The vectorisation operations and the commutation...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1973
ISSN: 0097-3165
DOI: 10.1016/0097-3165(73)90025-3