Shorted operators and rank decomposition matrices
نویسندگان
چکیده
منابع مشابه
Spectral Shorted Matrices
Given a n × n positive semidefinite matrix A and a subspace S of C, Σ(S, A) denotes the shorted matrix of A to S. We consider the notion of spectral shorted matrix ρ(S, A) = lim m→∞ Σ(S, A). We completely characterize this matrix in terms of S and the spectrum and the eigenspaces of A. We show the relation of this notion with the spectral order of matrices and the Kolmogorov’s complexity of A t...
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Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and 〈 , 〉A : H×H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), 〈ξ, η〉A = 〈Aξ, η〉, ξ, η ∈ H. Given T ∈ L(H), T is A-selfadjoint if AT = T ∗A. If S ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S, P(A,S) = {Q ∈ L(H) : Q = Q , R(Q) = S , AQ = Q∗A} for different choi...
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In this paper we study shorted operators relative to two different subspaces, for bounded operators on infinite dimensional Hilbert spaces. We define two notions of “complementability” in the sense of Ando for operators, and study the properties of the shorted operators when they can be defined. We use these facts in order to define and study the notions of parallel sum and subtraction, in this...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1986
ISSN: 0024-3795
DOI: 10.1016/0024-3795(86)90257-0