Theorems · Theorem · linear algebra
Matrix.PosDef.posSemidef_add
∀ {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.PosSemidef → B.PosDef → (A + B).PosDef- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Matrixstatement and proof · cited by 4,303
- StarRingstatement and proof · cited by 1,686
- add_commproof · cited by 1,535
- AddLeftMonostatement and proof · cited by 687
- Matrix.PosSemidefstatement and proof · cited by 76
- Matrix.PosDefstatement and proof · cited by 68
- Matrix.PosDef.add_posSemidefproof · cited by 2
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