Theorems · Theorem · functional analysis

RKHS.OfKernel.kernel_ofKernel

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {X : Type u_2} {V : Type u_3} [inst_1 : NormedAddCommGroup V]
  [inst_2 : InnerProductSpace 𝕜 V] [inst_3 : CompleteSpace V] {K : Matrix X X (V →L[𝕜] V)} [inst_4 : Fact K.PosSemidef],
  RKHS.kernel (RKHS.OfKernel K) = K

The kernel of the reproducing kernel Hilbert space generated by a positive semidefinite matrix is the original positive semidefinite matrix.

Defined in

Mathlib.Analysis.InnerProductSpace.Reproducing

Cited by

0 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpaceFact