Theorems · Theorem · operator theory
InnerProductSpace.trace_rankOne
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
[FiniteDimensional 𝕜 E] (x y : E), (LinearMap.trace 𝕜 E) ↑(((InnerProductSpace.rankOne 𝕜) x) y) = inner 𝕜 y x- Defined in
- Mathlib.Analysis.InnerProductSpace.Trace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement and proof · cited by 10,215
- ContinuousLinearMapstatement and proof · cited by 5,352
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- Finset.sum_congrproof · cited by 2,323
- FiniteDimensionalstatement and proof · cited by 1,854
- one_smulproof · cited by 1,374
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