Theorems · Theorem · linear algebra
Matrix.PosDef.add_posSemidef
∀ {m : Type u_1} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [AddLeftMono R]
{A B : Matrix m m R}, A.PosDef → B.PosSemidef → (A + B).PosDef- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Star.starproof · cited by 1,082
- AddLeftMonostatement and proof · cited by 687
- Finsupp.sumproof · cited by 481
- mul_addproof · cited by 413
- add_mulproof · cited by 363
- Matrix.PosSemidefstatement and proof · cited by 76
- Matrix.PosDefstatement and proof · cited by 68
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.PosDef.addproof · cited by 1
- Matrix.PosDef.posSemidef_addproof · cited by 0