Theorems · Theorem · combinatorics
SimpleGraph.posSemidef_lapMatrix
∀ {V : Type u_1} (R : Type u_2) [inst : Fintype V] (G : SimpleGraph V) [inst_1 : DecidableRel G.Adj]
[inst_2 : DecidableEq V] [inst_3 : Field R] [inst_4 : LinearOrder R] [IsStrictOrderedRing R] [inst_6 : StarRing R]
[TrivialStar R], (SimpleGraph.lapMatrix R G).PosSemidefThe Laplacian matrix is positive semidefinite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Matrixproof · cited by 4,303
- Finset.univproof · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Nat.cast_zeroproof · cited by 1,870
- StarRingstatement and proof · cited by 1,686
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Matrix.mulVecproof · cited by 267
- dotProductproof · cited by 194
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_reachableproof · cited by 2
- SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_adjproof · cited by 1