Theorems · Theorem · functional analysis
RCLike.mul_conj
∀ {K : Type u_1} [inst : RCLike K] (z : K), z * (starRingEnd K) z = ↑‖z‖ ^ 2- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- Realproof · cited by 25,697
- RingHomstatement · cited by 10,189
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapproof · cited by 4,706
- RCLikestatement and proof · cited by 2,829
- add_zeroproof · cited by 2,707
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- map_mulproof · cited by 1,137
- map_addproof · cited by 964
Cited by10
Results whose statement or proof uses this declaration.
- RCLike.conj_mulproof · cited by 10
- RCLike.inv_defproof · cited by 2
- InnerProductSpace.Core.inner_mul_inner_self_leproof · cited by 2
- RCLike.re_eq_norm_of_mul_conjproof · cited by 2
- Orthonormal.sum_inner_products_leproof · cited by 2
- InnerProductSpace.Core.cauchy_schwarz_auxproof · cited by 1
- entry_norm_bound_of_unitaryproof · cited by 1
- Complex.mul_conj'proof · cited by 1
- ContinuousLinearMap.reApplyInnerSelf_smulproof · cited by 1
- OrthonormalBasis.det_to_matrix_orthonormalBasisproof · cited by 0