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Theorems · Theorem · probability

ProbabilityTheory.covarianceBilin_multivariateGaussian

∀ {ι : Type u_1} [inst : Fintype ι] [inst_1 : DecidableEq ι] {μ : EuclideanSpace ℝ ι} {S : Matrix ι ι ℝ},
  S.PosSemidef →
    ∀ (x y : EuclideanSpace ℝ ι),
      ((ProbabilityTheory.covarianceBilin (ProbabilityTheory.multivariateGaussian μ S)) x) y = x.ofLp ⬝ᵥ S.mulVec y.ofLp
Defined in
Mathlib.Probability.Distributions.Gaussian.Multivariate
Cited by
3 results in Mathlib
Foundations
Depth 317 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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ProbabilityTheory.covariance_eval_multivariateGaussian · cited by 3ProbabilityTheory.covaria…ProbabilityTheory.measurePreserving_restrict₂_multivariateGaussian · cited by 1ProbabilityTheory.measure…ProbabilityTheory.charFun_multivariateGaussian · cited by 0ProbabilityTheory.charFun…DFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealRingHom.id · cited by 18349RingHom.idMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealFintype · cited by 7736FintypeContinuousLinearMap · cited by 5352ContinuousLinearMapMatrix · cited by 4303Matrixmap_mul · cited by 1137map_mulInner.inner · cited by 1089Inner.innerMeasureTheory.Measure.map · cited by 858Measure.mapWithLp.ofLp · cited by 323WithLp.ofLpEuclideanSpace · cited by 307EuclideanSpaceMatrix.mulVec · cited by 267Matrix.mulVecdotProduct · cited by 194dotProductProbabilityTheory.covarianceB…CITED BYCITES

Cites40

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Cited by3

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