摘要 : A square matrix is called Hessenberg whenever each entry below the subdiagonal is zero and each entry on the subdiagonal is nonzero. Let V denote a nonzero finite-dimensional vector space over a field K. We consider an ordered pai... 展开 A square matrix is called Hessenberg whenever each entry below the subdiagonal is zero and each entry on the subdiagonal is nonzero. Let V denote a nonzero finite-dimensional vector space over a field K. We consider an ordered pair of linear transformations A : V -> V and A* : V -> V which satisfy both (i) and (ii) below. (i) There exists a basis for V with respect to which the matrix representing A is Hessenberg 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 Hessenberg. We call such a pair a thin Hessenberg pair (or TH pair). This is a special case of a Hessenberg pair which was introduced by the author in an earlier paper. We investigate several bases for V with respect to which the matrices representing A and A* are attractive. We display these matrices along with the transition matrices relating the bases. We introduce an "oriented" version of A, A* called a TH system. We classify the TH systems up to isomorphism. 收起