Bezoutians and projections
نویسندگان
چکیده
منابع مشابه
Pseudorational Behaviors and Bezoutians
Behavioral system theory has been successful in providing a viewpoint that does not depend on a priori notions of inputs/outputs. While there are some attempts to extend this theory to infinite-dimensional systems, for example, delay systems, the overall picture seems to remain still incomplete. The first author has studied a class of infinite-dimensional systems called pseudorational. This cla...
متن کاملComputing Approximate Radicals using Bezoutians
Consider I ⊂ C[x1, . . . , xm], a zero dimensional complete intersection ideal, with I = (f1, . . . , fm). Assume that I has clusters of roots, each cluster of radius at most ε in the ∞-norm. We compute the “approximate radical” of I, i.e. an ideal which contains one root for each cluster, corresponding to the center of gravity of the points in the cluster, up to an error term asymptotically bo...
متن کاملA Proof of the Main Theorem on Bezoutians
where gcd stands for greatest common divisor. H. Wimmer in [8] attributes this result to Jacobi who in 1836 showed that the singularity of what we call the Bezoutian implies the existence of a common factor of f and g. More contemporary proofs of (1) can be found in the recent books [3, Theorems 21.10 and 21.11] by H. Dym and [5, Theorem 8.30] by P. Fuhrmann. In the Introduction to [3, Chapter ...
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It is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman-Magidor-Shelah [10]. We consider several antichain-catching properties that are weaker than saturation, and prove: (1) If I is a normal ideal on ω2 which satisfies stationary antichain catching, then there is an inner model with a Woodin cardinal; (2) For any n ∈ ω, it is consistent...
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We use unified algebraic methods to investigate the properties of polynomial Bezoutians with respect to a general basis. Not only can three known results be easily verified, but also some new properties of polynomial Bezoutians are obtained. Nonsymmetric Lyapunov-type equations of polynomial Bezoutians are also discussed. It turns out that most properties of classical Bezoutians can be analogou...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1984
ISSN: 0024-3795
DOI: 10.1016/0024-3795(84)90156-3