Theorems · Definition · functional analysis

InnerProductSpace.induced

{𝕜 : Type u_1} →
  {E : Type u_2} →
    [inst : RCLike 𝕜] →
      {G : Type u_4} →
        [inst_1 : SeminormedAddCommGroup E] →
          [inst_2 : InnerProductSpace 𝕜 E] →
            [inst_3 : AddCommGroup G] →
              [inst_4 : Module 𝕜 G] →
                {F : Type u_5} →
                  [inst_5 : FunLike F G E] → [inst_6 : LinearMapClass F 𝕜 G E] → (f : F) → InnerProductSpace 𝕜 G

A linear map from a Module to an InnerProductSpace induces an InnerProductSpace structure on the domain using the SeminormedAddCommGroup.induced norm. See note [reducible non-instances].

Defined in

Mathlib.Analysis.InnerProductSpace.Basic

Cited by

1 results in Mathlib

Foundations

Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpaceAddCommGroupModuleFunLikeLinearMapClass