Two linear transformations each tridiagonal with respect to an eigenbasis of the other ; an overview

@inproceedings{Terwilliger2003TwoLT,
  title={Two linear transformations each tridiagonal with respect to an eigenbasis of the other ; an overview},
  author={Paul Terwilliger},
  year={2003}
}
Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider an ordered pair of linear transformations A : V → V and A∗ : V → V that satisfy conditions (i), (ii) below. (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A∗ is diagonal. (ii) There exists a basis for V with respect to which the matrix representing A is diagonal and the matrix representing A∗ is irreducible… CONTINUE READING