Linear and multilinear algebra; matrix theory Vector spaces Concept
Linear subspace
Summary
A linear subspace of a vector space is a subset that contains the zero vector and is closed under addition and scalar multiplication. It is a vector space with the same operations.
Where this leads
37 pages build on this one.
- Graph of an operator
- Complemented subspace
- Interlacing of zeros of orthogonal polynomials
- Griffiths transversality
- Schubert calculus
- Witt group
- Cauchy interlacing theorem
- Courant–Fischer characterization of characteristic values
- Banach limit
- Existence of best approximations from finite-dimensional subspaces
- Quotient of a normed space
- Rayleigh–Ritz method
- Witt's theorem
- Courant–Fischer min-max theorem
- Grassmannian
- Schubert variety
- M. Riesz extension theorem
- Bott's Morse-theoretic proof of periodicity
- Krylov subspace
- Min-max theorem
- Polarity
- Projective space
- Lattice of subspaces
- Kolmogorov criterion for best approximation
- Dual operator
- Unbounded operator
- Dvoretzky's theorem
- LOBPCG
- Lorentz's characterization of almost convergence
- Hahn–Banach theorem
- Weyl's inequality
- Coplanarity
- Period map
- Projective subspace
- Cartan's test for involutivity
- Cartan–Kähler theorem
- Flag variety
Further reading
About this page
| Tag | 00YC1D652K |
|---|---|
| URI | m2://00YC1D652K |
| Aliases | vector-subspace |
| Kind | concept |
| Writing | W1 stated |
| MSC | 15A03 |
| Specializes | Vector space |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Special cases
- Column space
- Row space
- Invariant subspace
- Annihilator of a subspace
- Linear span
- Sum of subspaces
- Null space
- Kernel of a linear map
- Image of a linear map
- Orthogonal complement
- Krylov subspace
- Attainable null space
Definitions
Used by
- Graph of an operator
- Complemented subspace
- Existence of best approximations from finite-dimensional subspaces
- Quotient of a normed space
- Witt's theorem
- Courant–Fischer min-max theorem
- Grassmannian
- M. Riesz extension theorem
- Krylov subspace
- Min-max theorem
- Polarity
- Projective space
- Lattice of subspaces
- Kolmogorov criterion for best approximation
- Unbounded operator
- Dvoretzky's theorem
- Hahn–Banach theorem
- Coplanarity
- Projective subspace