薄的海森伯格对的可裂基

The Split Basis of a Thin Hessenberg Pair

设A,A*是薄的海森伯格对,则存在V的可裂基,使得A在这组基下的矩阵是下两对角矩阵,A*在这组基下的矩阵是上两对角矩阵.给出了在这组基下一些矩阵的关系式和A,A*的本原幂等元的表达式.最后,给出了可分序列的关系式.

In this paper we discuss thin Hessenberg pair A,A＊. It is known that there exists a basis for V with respect to which the matrix representing A is lower bidiagonal and the matrix representing A＊ is upper bidiagonal. We give some formulae involving the matrix units associated with this basis. We also dis- play some related formulae involving the primitive idempotents of A and A＊ and some formulae for the split sequences.