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Everything about Complemented subspace
Concept in functional analysis
In the branch of mathematics called functional analysis, a complemented subspace of a topological vector space is a vector subspace for which there exists some other vector subspace of called its (topological) complement in, such that is the direct sum in the category of topological vector spaces. Formally, topological direct sums strengthen the algebraic direct sum by requiring certain maps be continuous; the result retains many nice properties from the operation of direct sum in finite-dimensional vector spaces. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Complemented subspaceA 5-minute orientation
- Skim a recent paper: High-Order Correlation Preserved Incomplete Multi-View Subspace ClusteringInfluential work since 2022
- Pick up a classic book: Introduction to topologyThe most-reprinted book on the subject
- Read the landmark paper: Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basicCited 67 times
- Go sideways: Direct sumA closely related topic
- Go sideways: Reflexive spaceA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basic
On complemented subspaces ofm
Complemented subspace-based weighted collaborative representation model for imbalanced learning
Imbalanced complemented subspace representation with adaptive weight learning
The complemented subspace problem revisited
The complemented subspace problem for C(K)-spaces: A counterexample
L 1 (μ,X) as a complemented subspace of its bidual
A Frechet-Schwartz Space with Basis having a Complemented Subspace without Basis
🆕 Influential since 2022
High-Order Correlation Preserved Incomplete Multi-View Subspace Clustering
Adversarial Incomplete Multiview Subspace Clustering Networks
BSF: Block Subspace Filter for Removing Narrowband and Wideband Radio Interference Artifacts in Single-Look Complex SAR Images
Complemented subspaces of Banach lattices
A sufficient condition for the sum of complemented subspaces to be complemented
📚 Books worth reading
Introduction to topologyBert Mendelson · 1962
Coding the MatrixPhilip N. Klein · 2013- 📕Classical Banach Spaces IJoram Lindenstrauss · 1977
Jordan Canonical FormSteven H. Weintraub · 2009
An introduction to multivariable mathematicsSimon, L. · 2008
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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