Theorems · Theorem · linear algebra
Matrix.PosSemidef.trace_nonneg
∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [inst_3 : Fintype n]
[AddLeftMono R] {A : Matrix n n R}, A.PosSemidef → 0 ≤ A.trace- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Matrixstatement and proof · cited by 4,303
- StarRingstatement and proof · cited by 1,686
- AddLeftMonostatement and proof · cited by 687
- Matrix.tracestatement · cited by 114
- Matrix.PosSemidefstatement and proof · cited by 76
- Fintype.sum_nonnegproof · cited by 4
- Matrix.PosSemidef.diag_nonnegproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.IsPositive.trace_nonnegproof · cited by 0