Theorems · Theorem · functional analysis
finrank_euclideanSpace
∀ {ι : Type u_1} {𝕜 : Type u_3} [inst : RCLike 𝕜] [inst_1 : Fintype ι],
Module.finrank 𝕜 (EuclideanSpace 𝕜 ι) = Fintype.card ι- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- RCLikestatement and proof · cited by 2,829
- Module.finrankstatement and proof · cited by 1,770
- Fintype.cardstatement and proof · cited by 1,386
- EuclideanSpacestatement and proof · cited by 307
- LinearEquiv.finrank_eqproof · cited by 65
- WithLp.linearEquivproof · cited by 29
- Module.finrank_fintype_fun_eq_cardproof · cited by 14
Cited by9
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.eigenvectorBasisproof · cited by 12
- Matrix.IsHermitian.eigenvalues₀proof · cited by 5
- Matrix.IsHermitian.mulVec_eigenvectorBasisproof · cited by 3
- EuclideanSpace.volume_ballproof · cited by 2
- Matrix.IsHermitian.eigenvalues_mem_spectrum_realproof · cited by 2
- Matrix.IsHermitian.eigenvalues₀_antitoneproof · cited by 1
- finrank_euclideanSpace_finproof · cited by 1
- EuclideanSpace.volume_ball_fin_threeproof · cited by 1
- EuclideanSpace.volume_ball_fin_twoproof · cited by 1