کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6416096 | 1631097 | 2016 | 6 صفحه PDF | دانلود رایگان |
Matrices A of order n having entries in the field F(x1,â¦,xn) of rational functions over a field F and characteristic polynomialdetâ¡(tIâA)=tn+x1tnâ1+â¯+xnâ1t+xn are studied. It is known that such matrices are irreducible and have at least 2nâ1 nonzero entries. Such matrices with exactly 2nâ1 nonzero entries are called Ma-Zhan matrices. Conditions are given that imply that a Ma-Zhan matrix is similar via a monomial matrix to a generalized companion matrix (that is, a lower Hessenberg matrix with ones on its superdiagonal, and exactly one nonzero entry in each of its subdiagonals). Via the Ax-Grothendieck Theorem (respectively, its analog for the reals) these conditions are shown to hold for a family of matrices whose entries are complex (respectively, real) polynomials.
Journal: Linear Algebra and its Applications - Volume 498, 1 June 2016, Pages 360-365