Thin Hessenberg pairs |
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Authors: | Ali Godjali |
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Institution: | Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706-1388, USA |
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Abstract: | 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 called a TH system. We classify the TH systems up to isomorphism. |
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Keywords: | 15A04 |
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