Linear map between vector spaces over the same field

Depends on

• Vector space over a field
• Field

Used by

• A linear map from a finite-dimensional normed space is bounded Corollary
• Lambda identity minus compact has index zero Corollary
• A bounded linear operator between normed spaces Definition
• A norm on a real vector space, the induced metric, and the dictionary with the metric axioms Definition
• Bilinear forms, and symmetric, skew-symmetric, and alternating bilinear forms Definition
• Character and maximal ideal space Definition
• Compact linear operator Definition
• Complexification of a real-linear map Definition
• Conjugations and real structures on a complex vector space Definition
• Coordinate columns [v]_B and matrices [T]_B^C of linear maps relative to ordered bases Definition
• Derivations of Lie algebras Definition
• Eigenvalues, eigenvectors, eigenspaces E_λ(T)=ker(T-λ I), and the spectrum σ_F(T) of an endomorphism Definition
• Homomorphisms of possibly infinite-dimensional Lie algebras Definition
• Infinitesimal generator of a unitary group Definition
• Intertwiners, the spaces Hom_G(V,W) and End_G(V), equivalent representations, and faithful representations Definition
• Invariant subspaces, restrictions, and induced quotient operators Definition
• Invertible linear maps, linear isomorphisms, and inverse linear maps Definition
• Kernel and image of a linear map Definition
• Lie algebras over a field Definition
• Lie-algebra homomorphism Definition
• Linear functionals and the algebraic dual V^*=L(V,F) Definition
• Linear isometries and isometric isomorphisms Definition
• Linear isometries, and orthogonal or unitary operators on finite-dimensional inner product spaces Definition
• Nilpotent endomorphisms and their nilpotency index Definition
• Resolvent and spectrum of an unbounded operator Definition
• Smooth vector bundles, rank, fibres, and trivial bundles Definition
• Spectrum and resolvent of a bounded operator Definition
• The adjoint T^*:W→ V is characterised by ⟨ Tv,w⟩_W=⟨ v,T^*w⟩_V Definition
• The pullback of a covariant tensor by a linear map Definition
• The space L(V,W) of linear maps with pointwise addition and scalar multiplication Definition
• The subspace Γ of directions along which a series converges absolutely, and its orthogonal complement Γ^⊥ Definition
• Unbounded linear operators: domain, graph and extension Definition
• Vector bundle maps over a smooth base map Definition
• A choice-free discontinuous linear functional on c₀0 Example
• Diagonal operator on ell p is compact iff diagonal tends to zero Example
• Fredholm alternative for an integral equation Example
• Frobenius reciprocity for group representations without tensor products Example
• The forward shift on F^ℕ is injective but not surjective Example
• A linear functional annihilating the kernel of a surjection is a unique transpose multiple Lemma
• A linear map preserves zero, negatives, and subtraction Lemma

…and 18 more results.

Dependency tree · two levels

8 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Axler, Linear Algebra Done Right, Chapter 3 (standard reference, not scraped)