منابع مشابه
Rank-deficient submatrices of Kronecker products of Fourier matrices
We provide a set of maximal rank-deficient submatrices of a Kronecker product of two matrices A ⊗ B, and in particular the Kronecker product of Fourier matrices F = Fn1 ⊗ . . . ⊗ Fnk . We show how in the latter case, maximal rank-deficient submatrices can be constructedas tilings of rank-one blocks. Such tilings exist for any subgroup of a suitable Abelian group associated to the matrix F . The...
متن کاملKronecker 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 کاملBoolean Products of Lattices
A study is made of Boolean product representations of bounded lattices over the Stone space of their centres. Special emphasis is placed on relating topological properties such as clopen or regular open equalizers to their equivalent lattice theoretic counterparts. Results are also presented connecting various properties of a lattice with properties of its individual stalks. Mathematics Subject...
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: Linear Algebra and its Applications
سال: 2001
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(01)00338-x