Theorems · Theorem · linear algebra
Matrix.posSemidef_sum
∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] {ι : Type u_5}
[AddLeftMono R] {x : ι → Matrix n n R} (s : Finset ι), (∀ i ∈ s, (x i).PosSemidef) → (∑ i ∈ s, x i).PosSemidef- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Finsuppproof · cited by 5,255
- Finset.sumstatement · cited by 5,195
- 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
- Finset.mul_sumproof · cited by 196
- Finset.sum_mulproof · cited by 112
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