Theorems · Theorem · linear algebra
Matrix.PosDef.transpose
∀ {n : Type u_2} {R' : Type u_4} [inst : CommRing R'] [inst_1 : PartialOrder R'] [inst_2 : StarRing R']
{M : Matrix n n R'}, M.PosDef → M.transpose.PosDef- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingPartialOrderStarRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- PartialOrderstatement and proof · cited by 6,410
- Finsuppproof · cited by 5,255
- Matrixstatement and proof · cited by 4,303
- StarRingstatement and proof · cited by 1,686
- MulZeroClass.zero_mulproof · cited by 1,625
- Star.starproof · cited by 1,082
- Finsupp.sumproof · cited by 481
- Matrix.transposestatement and proof · cited by 389
- star_starproof · cited by 135
- Finsupp.mapRangeproof · cited by 91
- Matrix.PosDefstatement and proof · cited by 68
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.PosDef.transpose_iffproof · cited by 1
- LDL.lowerInv_eq_gramSchmidtBasisstatement and proof · cited by 0