Theorems · Theorem · functional analysis

ContinuousLinearMap.ker_le_ker_iff_range_le_range

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  [FiniteDimensional 𝕜 E] {T U : E →L[𝕜] E},
  (↑T).IsSymmetric → (↑U).IsSymmetric → ((↑U).ker ≤ (↑T).ker ↔ (↑T).range ≤ (↑U).range)

Defined in

Mathlib.Analysis.InnerProductSpace.Adjoint

Cited by

0 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFiniteDimensional