Polynomial Properties in Unitriangular Matrices
نویسندگان
چکیده
منابع مشابه
Commutators and powers of infinite unitriangular matrices
In the paper we consider some commutator-type and power-type matrix equations in the group UT(∞,K) of infinite dimensional unitriangular matrices over a fieldK. We introduce a notion of a power outer commutator ω1k k (x1, ..., xk) and a power Engel commutator e1k k (x, y) as outer (respectively Engel) commutators modified by allowing powers of letters instead of letters alone. For a given infin...
متن کاملHopf monoids from class functionson unitriangular matrices
We build, from the collection of all groups of unitriangular matrices, Hopf monoids in Joyal’s category of species. Such structure is carried by the collection of class function spaces on those groups, and also by the collection of superclass function spaces, in the sense of Diaconis and Isaacs. Superclasses of unitriangular matrices admit a simple description from which we deduce a combinatori...
متن کاملSome Properties of Laurent Polynomial Matrices
In the context of multivariate signal processing, factorizations involving so-called para-unitary matrices are relevant as well demonstrated in the book of Vaidyanathan [11], or [4, 1] and more recently in a series of papers by McWhirter and co-authors [5, 6]. However, known factorizations of matrix polynomials, such as the Smith form [10], involve unimodular matrices but usual factorizations s...
متن کاملRational and Polynomial Matrices
where λ = s or λ = z for a continuousor discrete-time realization, respectively. It is widely accepted that most numerical operations on rational or polynomial matrices are best done by manipulating the matrices of the corresponding descriptor system representations. Many operations on standard matrices (such as finding the rank, determinant, inverse or generalized inverses, nullspace) or the s...
متن کاملSome results on the polynomial numerical hulls of matrices
In this note we characterize polynomial numerical hulls of matrices $A in M_n$ such that$A^2$ is Hermitian. Also, we consider normal matrices $A in M_n$ whose $k^{th}$ power are semidefinite. For such matriceswe show that $V^k(A)=sigma(A)$.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8896