We introduce the concept of a morphism from the set of Butson Hadamard matrices over k th roots of unity to the set of Butson matrices over l roots of unity. As concrete examples of such morphisms, we describe tensor-product-like maps which reduce the order of the roots of unity appearing in a Butson matrix at the cost of increasing the dimension. Such maps can be constructed from Butson matric...

The chromatic polynomials of certain families of graphs can be calculai ed by a transfer matrix method. The transfer matrix commutes with an action of the symmetric group on the colours. Using représentation theory, it is shown that the matrix is équivalent to a block-diagonal matrix. The multiplicities and the sizes of the blocks are obtained. Using a repeated inclusion-exclusion argument the ...

Abstract Monotone matrices are stochastic that satisfy the monotonicity conditions as introduced by Daley in 1968. Markov chains useful modeling phenomena several areas. Most previous work examines embedding problem for within entire set of transition matrices, and only a few studies focus on embeddability specific subset matrices. This article discrete-time monotone chain, i.e., existence matr...

The tropical roots of t×p(x) = max0≤j≤` ‖Aj‖x are points at which the maximum is attained at least twice. These roots, which can be computed in only O(`) operations, can be good approximations to the moduli of the eigenvalues of the matrix polynomial P (λ) = ∑` j=0 λ Aj , in particular when the norms of the matrices Aj vary widely. Our aim is to investigate this observation and its applications...

A little known property of determinants is developed in a manner accessible to beginning undergraduates in linear algebra. Using the language of matrix theory, a classical result by Sylvester that describes when two polynomials have a common root is recaptured. Among results concerning the structure of polynomial roots, polynomials with pairs of roots that are either multiplicative inverses or ...