Theorems · Theorem · linear algebra
Matrix.PosDef.diagonal
∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R]
[inst_4 : DecidableEq n] [NoZeroDivisors R] {d : n → R}, (∀ (i : n), 0 < d i) → (Matrix.diagonal d).PosDef- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Finsuppproof · cited by 5,255
- LT.lt.leproof · cited by 2,189
- MulZeroClass.mul_zeroproof · cited by 2,091
- StarRingstatement and proof · cited by 1,686
- MulZeroClass.zero_mulproof · cited by 1,625
- Star.starproof · cited by 1,082
- Finsupp.supportproof · cited by 828
- StarOrderedRingstatement and proof · cited by 587
- NoZeroDivisorsstatement and proof · cited by 545
Cited by4
Results whose statement or proof uses this declaration.
- Matrix.PosDef.oneproof · cited by 2
- Matrix.posDef_diagonal_iffproof · cited by 2
- Matrix.PosDef.natCastproof · cited by 1
- Matrix.PosDef.intCastproof · cited by 0