Theorems · Theorem · linear algebra
LDL.lowerInv_orthogonal
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {n : Type u_2} [inst_1 : LinearOrder n] [inst_2 : WellFoundedLT n]
[inst_3 : LocallyFiniteOrderBot n] {S : Matrix n n 𝕜} [inst_4 : Fintype n] (hS : S.PosDef) {i j : n},
i ≠ j → inner 𝕜 (WithLp.toLp 2 (LDL.lowerInv hS i)) (WithLp.toLp 2 (S.transpose.mulVec (LDL.lowerInv hS j))) = 0- Defined in
- Mathlib.Analysis.Matrix.LDL
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- ENNRealstatement · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement · cited by 1,089
- WellFoundedLTstatement and proof · cited by 491
- Matrix.transposestatement · cited by 389
- WithLpstatement · cited by 345
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Matrix.mulVecstatement · cited by 267
Cited by1
Results whose statement or proof uses this declaration.
- LDL.diag_eq_lowerInv_conjproof · cited by 1