Central polynomials for matrix rings

Differential Polynomial Rings of Triangular Matrix Rings

Central polynomials for matrix algebras over the Grassmann algebra

In this work, we describe a method to construct central polynomials for F -algebras where F is a field of characteristic zero. The main application deals with the T -prime algebras Mn(E), where E is the infinitedimensional Grassmann algebra over F , which play a fundamental role in the theory of PI-algebras. The method is based on the explicit decomposition of the group algebra FSn. AMS Classif...

Fast methods for resumming matrix polynomials and Chebyshev matrix polynomials

Fast and effective algorithms are discussed for resumming matrix polynomials and Chebyshev matrix polynomials. These algorithms lead to a significant speed-up in computer time by reducing the number of matrix multiplications required to roughly twice the square root of the degree of the polynomial. A few numerical tests are presented, showing that evaluation of matrix functions via polynomial e...

Higher numerical ranges of matrix polynomials

 Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical...

Generalized numerical ranges of matrix polynomials

In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.