Theorems · Theorem · functional analysis
CStarModule.norm_sq_eq
∀ (A : Type u_1) {E : Type u_2} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [inst_2 : AddCommGroup E]
[inst_3 : Module ℂ E] [inst_4 : SMul A E] [inst_5 : Norm E] [inst_6 : CStarModule A E] {x : E},
‖x‖ ^ 2 = ‖inner A x x‖- Cited by
- 5 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- StarRingproof · cited by 1,686
- Inner.innerstatement and proof · cited by 1,089
- Normstatement and proof · cited by 512
- NonUnitalSemiringproof · cited by 339
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- Real.sq_sqrtproof · cited by 53
Cited by5
Results whose statement or proof uses this declaration.
- WithCStarModule.norm_apply_le_normproof · cited by 2
- WithCStarModule.norm_singleproof · cited by 1
- WithCStarModule.pi_norm_le_sum_normproof · cited by 0
- CStarMatrix.norm_le_of_forall_inner_leproof · cited by 0
- WithCStarModule.prod_norm_le_norm_addproof · cited by 0