Theorems · Theorem · linear algebra
Matrix.posDef_sum
∀ {m : Type u_1} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] {ι : Type u_5}
[AddLeftMono R] {A : ι → Matrix m m R} {s : Finset ι}, s.Nonempty → (∀ i ∈ s, (A i).PosDef) → (∑ i ∈ s, A i).PosDef- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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
- Finset.sumstatement and proof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- add_zeroproof · cited by 2,707
- Finset.sum_congrproof · cited by 2,323
- StarRingstatement and proof · cited by 1,686
- Finset.Nonemptystatement and proof · cited by 1,001
- AddLeftMonostatement and proof · cited by 687
- Finset.sum_insertproof · cited by 196
- Finset.induction_onproof · cited by 167
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