Resultants, companion matrices, and Jacobson chains
نویسندگان
چکیده
منابع مشابه
Nil-clean Companion Matrices
The classes of clean and nil-clean rings are closed with respect standard constructions as direct products and (triangular) matrix rings, cf. [12] resp. [4], while the classes of weakly (nil-)clean rings are not closed under these constructions. Moreover, while all matrix rings over fields are clean, [12] when we consider nil-clean rings there are strongly restrictions: if a matrix ring over a ...
متن کاملLinear Construction of Companion Matrices
This note is concerned with the following problem: For a given matrix A E C’Ix” and a vector a E C”, does there exist a mapping 2’ assigning to each manic polynomial f of degree n a vector X(f) E C” such that the matrix B := A a. X(f)’ is a companion matrix off, i.e., the characteristic polynomial of B is t l)“ftf’ The classes of suitable matrices A and vectors a are characterized, and some pro...
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Given integers t , k, and v such that 0 t k v, let Wtk(v) be the inclusion matrix of t-subsets vs. k-subsets of a v-set. We modify slightly the concept of standard tableau to study the notion of rank of a finite set of positive integers which was introduced by Frankl. Utilizing this, a decomposition of the poset 2[v] into symmetric skipless chains is given. Based on this decomposition, we const...
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Article history: Received 15 December 2010 Accepted 10 May 2011 Available online 21 June 2011 Submitted by R.A. Brualdi AMS classification: 05A15 15A06 39A05
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We show that the usual companion matrix of a polynomial of degree n can be factored into a product of n matrices, n− 1 of them being the identity matrix in which a 2 × 2 identity submatrix in two consecutive rows (and columns) is replaced by an appropriate 2 × 2 matrix, the remaining being the identity matrix with the last entry replaced by possibly different entry. By a certain similarity tran...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1987
ISSN: 0024-3795
DOI: 10.1016/0024-3795(87)90075-9