摘要 : Let K denote a field and V denote a nonzero finite-dimensional vector space over K. We consider an ordered pair of linear transformations A : V -> V and A* : V -> V that satisfy (i)-(iii) below. (i) Each of A, A* is diagonalizable... 展开 Let K denote a field and V denote a nonzero finite-dimensional vector space over K. We consider an ordered pair of linear transformations A : V -> V and A* : V -> V that satisfy (i)-(iii) below. (i) Each of A, A* is diagonalizable on V. (ii) There exists an ordering {V-i}(i=0)(d) that A*V-i subset of V-0 + V-1 + ... + Vi+1 (0 <= i <= d). where V-1 = 0, Vd+1 = 0. (iii) There exists an ordering {V-i*}(i=0)(delta) of the eigenspaces of A* such that AV(i)* subset of V-0* + V-1* + ... + Vi+1* (0 <= i <= delta), where V-1* = 0,V delta+1* = 0. We call such a pair a Hessenberg pair on V. In this paper we obtain some characterizations of Hessenberg pairs. We also explain how Hessenberg pairs are related to tridiagonal pairs. 收起