Topic
Linear span
About: Linear span is a research topic. Over the lifetime, 632 publications have been published within this topic receiving 11691 citations. The topic is also known as: linear hull & span.
Papers published on a yearly basis
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Papers
TL;DR: In this paper, a measure on the closed subspaces of a Hilbert space is defined, which assigns to every closed subspace a non-negative real number such that if the subspace is a countable collection of mutually orthogonal sub-spaces having closed linear span B, then
Abstract: In his investigations of the mathematical foundations of quantum mechanics, Mackey1 has proposed the following problem: Determine all measures on the closed subspaces of a Hilbert space. A measure on the closed subspaces means a function μ which assigns to every closed subspace a non-negative real number such that if {Ai} is a countable collection of mutually orthogonal subspaces having closed linear span B, then
$$ \mu (B) = \sum {\mu \left( {{A_i}} \right)} $$
.
1,410 citations
TL;DR: This note shows that the second objection can be amended by combining some ideas used before in [2], and the present and previous results are expressed by the following lemma’s and theorem.
493 citations
TL;DR: In this paper, the concept of invariance of a subspace under a linear transformation is strongly connected with controllability and observability of linear dynamical systems, and the authors define controlled and conditioneded invariant subspaces as a generalization of the simple invariants, for the purpose of investigating some further structural properties of linear systems.
Abstract: The concept of invariance of a subspace under a linear transformation is strongly connected with controllability and observability of linear dynamical systems. In this paper, we definecontrolled andconditioned invariant subspaces as a generalization of the simple invariants, for the purpose of investigating some further structural properties of linear systems. Moreover, we prove some fundamental theorems on which the computation of the above-mentioned subspaces is based. Then, we give two examples of practical application of the previous concepts concerning the determination of the constant output and perfect output controllability subspaces.
429 citations
TL;DR: In this paper, the authors studied the robustness of fusion frame systems and proposed a weighted and distributed processing technique for fusion frames, which is a natural fit to distributed processing systems such as sensor networks, but also an efficient scheme for parallel processing of very large frame systems.
428 citations
TL;DR: In this paper, it was shown that unless @s is itself a polynomial, it is possible to uniformly approximate any continuous function on R^s arbitrarily well on every compact subset of R^ s by functions in this span.
302 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 3 |
| 2023 | 4 |
| 2022 | 27 |
| 2021 | 17 |
| 2020 | 21 |