Theorems · Theorem · linear algebra
Matrix.PosSemidef.diag_nonneg
∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] {A : Matrix n n R},
A.PosSemidef → ∀ {i : n}, 0 ≤ A i i- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 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.
Cites15
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
- Matrixstatement and proof · cited by 4,303
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- 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.singleproof · cited by 943
- Finsupp.sumproof · cited by 481
- Finsupp.sum_single_indexproof · cited by 130
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.PosSemidef.trace_nonnegproof · cited by 1