Theorems · Theorem · linear algebra
Matrix.PosDef.posSemidef
∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] {M : Matrix n n R},
M.PosDef → M.PosSemidef- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingPartialOrderStarRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Finsuppproof · cited by 5,255
- Matrixstatement and proof · cited by 4,303
- StarRingstatement and proof · cited by 1,686
- eq_or_neproof · cited by 1,117
- Matrix.PosSemidefstatement · cited by 76
- Matrix.PosDefstatement and proof · cited by 68
- Finsupp.sum_fun_zeroproof · cited by 29
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.isStrictlyPositive_iff_posDefproof · cited by 2
- Matrix.PosDef.kroneckerproof · cited by 1
- Matrix.PosDef.fromBlocks₁₁proof · cited by 1
- Matrix.PosDef.addproof · cited by 1
- LDL.lowerInv_eq_gramSchmidtBasisstatement and proof · cited by 0