On the bilinear transformation of companion matrices
B.A. Shane,Stephen Barnett +1 more
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TLDR
In this paper, it was shown that the matrix obtained by applying a matrix bilinear transformation to a companion matrix can itself be transformed by a similarity transformation into a companion matrices, using a matrix T which is invariant for matrices of a particular order.About:
This article is published in Linear Algebra and its Applications.The article was published on 1974-01-01 and is currently open access. It has received 4 citations till now. The article focuses on the topics: Square matrix & Companion matrix.read more
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On functions of companion matrices
TL;DR: In this paper, some new properties of a function f(C) of a companion matrix C, including a representation of any entry of F as a divided difference of f(λ) times a polynomial, were presented.
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Location of matrix eigenvalues in the complex plane
S. Barnett,R. Scraton +1 more
TL;DR: In this article, the problem of locating the eigenvalues of A relative to S can be transformed into that for an appropriate block companion matrix relative to R by a rational transformation.
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Algorithms for Classical Stability Problems
TL;DR: In this article, special numerical integration formulas are developed which transform a differential equation into a difference equation, such that the differential equation and the corresponding difference equation are both stable or else they are both unstable.
Journal ArticleDOI
Some applications of matrices to location of zeros of polynomials
TL;DR: In this paper, the location of zeros of a polynomial with respect to the left half plane Γ 1 or the unit circle Γ 2 has been reformulated more simply in terms of appropriate companion matrices.