Theorems · Theorem · functional analysis
SchauderBasis.finrank_range_proj
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {X : Type u_2} [inst_1 : NormedAddCommGroup X]
[inst_2 : NormedSpace 𝕜 X] (b : SchauderBasis 𝕜 X) (n : ℕ), Module.finrank 𝕜 ↥(↑(b.proj n)).range = nThe dimension of the range of the projection P n is n.
- Defined in
- Mathlib.Analysis.Normed.Module.Bases
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Submodulestatement · cited by 7,192
- ContinuousLinearMapproof · cited by 5,352
- Module.finrankstatement and proof · cited by 1,770
- Finset.rangeproof · cited by 1,341
- LinearMap.rangestatement and proof · cited by 893
- ContinuousLinearMap.toLinearMapstatement and proof · cited by 528
- Finset.card_rangeproof · cited by 108
- SchauderBasis.projstatement · cited by 13
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