Multi-companion matrices
نویسندگان
چکیده
منابع مشابه
Singular value decomposition of multi-companion matrices
We obtain the singular value decomposition of multi-companion matrices. We completely characterise the columns of the matrix U and give a simple formula for obtaining the columns of the other unitary matrix, V , from the columns of U . We also obtain necessary and sufficient conditions for the related matrix polynomial to be hyperbolic.
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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 ...
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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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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: 2002
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(01)00475-x