Theorems · Theorem · functional analysis
Complex.isometryOfOrthonormal_apply
∀ {F : Type u_5} [inst : NormedAddCommGroup F] [inst_1 : InnerProductSpace ℝ F] (v : OrthonormalBasis (Fin 2) ℝ F)
(z : ℂ), (Complex.isometryOfOrthonormal v) z = z.re • v 0 + z.im • v 1- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Complexstatement and proof · cited by 5,565
- InnerProductSpacestatement and proof · cited by 3,523
- Complex.restatement and proof · cited by 882
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- LinearIsometryEquivstatement · cited by 748
- Complex.imstatement and proof · cited by 591
- EuclideanSpaceproof · cited by 307
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