A natural family of quantized matrix algebras is introduced. It includes the two best studied such. Located inside U q (A 2n?1), it consists of quadratic algebras with the same Hilbert series as polynomials in n 2 variables. We discuss their general properties and investigate some members of the family in great detail with respect to associated varieties, degrees, centers, and symplectic leaves...

ALEXANDRA NASCIMENTO BAPTISTA Department of Mathematics, School of Technology and Management, Polytechnic Institute of Leiria, Campus 2, Morro do Lena – Alto do Vieiro, 2411-901, Leiria, Portugal Centro de Investigação em Matemática e Aplicações, University of Évora, Rua Romão Ramalho, 59, 7000-671, Évora, Portugal CARLOS CORREIA RAMOS Centro de Investigação em Matemática e Aplicações, Departme...

Applying a few steps of the Arnoldi process to a large nonsymmetric matrix A with initial vector v is shown to induce several quadrature rules. Properties of these rules are discussed, and their application to the computation of inexpensive estimates of the quadratic form 〈f, g〉 := v∗(f(A))∗g(A)v and related quadratic and bilinear forms is considered. Under suitable conditions on the functions ...

The T-palindromic quadratic eigenvalue problem (λB + λC + A)x = 0, with A,B,C ∈ Cn×n, C = C and B = A, governs the vibration behavior of trains. One way to solve the problem is to apply a structure-preserving doubling algorithm (SDA) to the nonlinear matrix equation (NME) X + BX−1A = C and “square-root” the matrix quadratic involved. In this paper, we generalize the SDA for the solution of (odd...