Theorems · Theorem · linear algebra
Matrix.PosSemidef.zero
∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R], Matrix.PosSemidef 0- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 1 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.
Cites12
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 · cited by 4,303
- MulZeroClass.mul_zeroproof · cited by 2,091
- StarRingstatement and proof · cited by 1,686
- MulZeroClass.zero_mulproof · cited by 1,625
- Star.starproof · cited by 1,082
- Finsupp.sumproof · cited by 481
- Matrix.PosSemidefstatement · cited by 76
- Finsupp.sum_fun_zeroproof · cited by 29
- Matrix.isHermitian_zeroproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.PosSemidef.invproof · cited by 2