Quasi-identities on matrices and the Cayley–Hamilton polynomial
نویسندگان
چکیده
منابع مشابه
Invariants and polynomial identities for higher rank matrices
We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct discriminants and the determinant as the discriminant of order d, where d is the dimension of the matrix. The characteristic polynomials and the Cayley–Hamilton th...
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 کاملSome Results on Polynomial Numerical Hulls of Perturbed Matrices
In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.
متن کاملThe Abel-Type Polynomial Identities
The Abel identity is (x + y) = n ∑ i=0 ( n i ) x(x − iz)i−1(y + iz)n−i, where x, y and z are real numbers. In this paper we deduce several polynomials expansions, referred to as Abel-type identities, by using Foata’s method, and also show some of their applications.
متن کاملAlgebras, Dialgebras, and Polynomial Identities *
This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for converting identities for algebras into identities for dialgebras; the BSO algorithm for converting oper...
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: Advances in Mathematics
سال: 2015
ISSN: 0001-8708
DOI: 10.1016/j.aim.2015.03.021