Hessenberg pairs of linear transformations

On One-Sided Ideals of Rings of Linear Transformations

Linear Transformations

The n×m matrix AT obtained by exchanging rows and columns of A is called the transpose of A. A matrix A is said to be symmetric if A = AT . The sum of two matrices of equal size is the matrix of the entry-by-entry sums, and the scalar product of a real number a and an m× n matrix A is the m× n matrix of all the entries of A, each multiplied by a. The difference of two matrices of equal size A a...

q-Inverting pairs of linear transformations and the q-tetrahedron algebra

As part of our study of the q-tetrahedron algebra ⊠q we introduce the notion of a q-inverting pair. Roughly speaking, this is a pair of invertible semisimple linear transformations on a finite-dimensional vector space, each of which acts on the eigenspaces of the other according to a certain rule. Our main result is a bijection between the following two sets: (i) the isomorphism classes of fini...

Some Further Transformations for Wp-bailey Pairs

Let (αn(a, k), βn(a, k)) be a WP-Bailey pair. Assuming the limits exist, let (α n(a), β ∗ n(a)) = lim k→1 ( αn(a, k), βn(a, k) 1− k ) be the derived WP-Bailey pair. By considering a particular limiting case of a transformation due to George Andrews, we derive some transformation and summation formulae for derived WP-Bailey pairs. We then use the formula to derive new identities for various thet...

on one-sided ideals of rings of linear transformations