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Everything about Linear subspace
In mathematics, vector subspace
In mathematics, and more specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Linear subspaceA 5-minute orientation
- Skim a recent paper: Linear Subspace Surrogate Modeling for Large-Scale Expensive Single/Multiobjective OptimizationInfluential work since 2022
- Pick up a classic book: Shift operators in Banach spaceThe most-reprinted book on the subject
- Read the landmark paper: Recursive subspace identification of linear and non-linear Wiener state-space modelsCited 179 times
- Go sideways: Kernel (linear algebra)A closely related topic
- Go sideways: Row and column spacesA closely related topic
📖 Definitions
Noun A subset of vectors of a vector space which is closed under the addition and scalar multiplication of that vector space.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Recursive subspace identification of linear and non-linear Wiener state-space models
Subspace identification of multivariable linear parameter-varying systems
Linear Subspace Learning-Based Dimensionality Reduction
Linear Subspace Ranking Hashing for Cross-Modal Retrieval
Linear subspace design for real-time shape deformation
Inexact Krylov Subspace Methods for Linear Systems
The Invariant Subspace Lattice of a Linear Transformation
Linear parameter-varying subspace identification: A unified framework
🆕 Influential since 2022
Linear Subspace Surrogate Modeling for Large-Scale Expensive Single/Multiobjective Optimization
Multi-orbit cyclic subspace codes and linear sets
Kernelized transformed subspace clustering with geometric weights for non-linear manifolds
t-Linear Tensor Subspace Learning for Robust Feature Extraction of Hyperspectral Images
Half-Dimension Subspace Decomposition for Fast Direction Finding With Arbitrary Linear Arrays
📚 Books worth reading
- 📕Shift operators in Banach spaceRalph Gellar · 1968
Treatise on the shift operatorN. K. Nikolʹskiĭ · 1986
A Celebration of Algebraic Geometry (Clay Mathematics Proceedings)Brendan Hassett, James McKernan · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Rank–nullity theorem The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity…
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