Projections in abstract sets
نویسندگان
چکیده
منابع مشابه
Witness sets of projections
Elimination is a basic algebraic operation which geometrically corresponds to projections. This article describes using the numerical algebraic geometric concept of witness sets to compute the projection of an algebraic set. The ideas described in this article apply to computing the image of an algebraic set under any linear map.
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Given a closed subspace S of a Hilbert space H and a bounded linear operator A ∈ L(H) which is positive, consider the set of all A-selfadjoint projections onto S P(A,S) = {Q ∈ L(H) : Q2 = Q , Q(H) = S , AQ = Q∗A}. In addition, if H1 is another Hilbert space, T : H → H1 is a bounded linear operator such that T ∗T = A and ξ ∈ H, consider the set of (T,S) spline interpolants to ξ: sp (T,S, ξ) = {η...
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Reconstructing Plane Sets from Projections
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Nonempty sets X1 and X2 in the Euclidean space R n are called homothetic provided X1 = z+λX2 for a suitable point z ∈ R n and a scalar λ 6= 0, not necessarily positive. Extending results of Süss and Hadwiger (proved by them for the case of convex bodies and positive λ), we show that compact (respectively, closed) convex sets K1 and K2 in R n are homothetic provided for any given integer m, 2 ≤ ...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1953
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-40-1-160-164