Inners and Schur complement
Stephen Barnett,E.I. Jury +1 more
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In this paper, it was shown that for any square matrix having a left triangle of zeros, the determinants of its inners are equal to the leading principal minors of its Schur complement.About:
This article is published in Linear Algebra and its Applications.The article was published on 1978-12-01 and is currently open access. It has received 11 citations till now. The article focuses on the topics: Schur's theorem & Schur complement.read more
Citations
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The roles of Sylvester and Bezoutian matrices in the historical study of stability of linear discrete-time systems
TL;DR: In this paper, a review of the early pioneering works of Hermite, Schur, Cohn, and Fujiwara, and how these paved the way for modern development of other criteria are indicated.
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On the Schur complement and the LU-factorization of a matrix
TL;DR: In this article, the Lu-factorization of a matrix could be used to study its Schur complements and vice-versa, and it is argued that the Schur complement provides a compact tool for studying problems rekated to the incomplete Choleski factorization.
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A note on the reduced Schur-Cohn criterion
E. I. Jury,Brian D. O. Anderson +1 more
TL;DR: In this paper, the reduced Schur-Cohn matrices of the symmetric matrices B for n -even and A -matrix for n-odd in connection with theorems l e and l o of [1] were simplified.
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Remarks on redundance in stability criteria and a counterexample to fullers conjecture
TL;DR: In this paper, it was shown that the [n(n+ l)/2] conditions for stability in the left-half plane as well as inside the unit circle as given by Routh and Jury-Gutman, can be reduced reapectively to {[n[n− 1/2] + l} and {n[ n− 1)/2 ] + 2} conditions.
Book ChapterDOI
Computing the Greatest Common Divisor of Polynomials Using the Comrade Matrix
TL;DR: The comrade matrix of a polynomial is an analogue of the companion matrix when the matrix is expressed in terms of a general basis such that the basis is a set of orthogonal polynomials satisfying the three-term recurrence relation.
References
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Manifestations of the Schur complement
TL;DR: In this paper, the Schur complement can be used in numerical linear algebra (NLAs) and the author is concerned with some of the ways in which it can be applied.
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Generalized Bezoutian and Sylvester matrices in multivariable linear control
Brian D. O. Anderson,E. Jury +1 more
TL;DR: In this article, generalized Bezoutian and Sylvester matrices are defined and discussed in a short paper, where the relationship between these two forms of matrices is established and it is shown that the degree of a real rational function can be ascertained by checking the rank of either one of these generalized matrices formed using a polynomial matrix fraction decomposition of the prescribed transfer function matrix.
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Greatest common divisor of several polynomials
TL;DR: In this paper, it was shown that the degree k of the greatest common divisor of the polynomials is equal to the rank defect of the matrix R = [b1(A, b2(A), …, bm(A)], where A is a suitable companion matrix of a(λ), and if the first k rows of R are expressed as linear combinations of the remaining n-k rows (which are linearly independent) then the coefficients of row k + 1 in these expressions.