Theorems · Theorem · linear algebra
Matrix.PosDef.trace_pos
∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [inst_3 : Fintype n]
[Nontrivial R] [IsOrderedCancelAddMonoid R] [Nonempty n] {A : Matrix n n R}, A.PosDef → 0 < A.trace- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- Finset.univproof · cited by 3,473
- Nontrivialstatement and proof · cited by 2,416
- StarRingstatement and proof · cited by 1,686
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- Matrix.tracestatement · cited by 114
- Matrix.PosDefstatement and proof · cited by 68
- Finset.univ_nonemptyproof · cited by 50
- Finset.sum_posproof · cited by 15
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