Theorems · Theorem · linear algebra
Matrix.PosSemidef.inv
∀ {n : Type u_2} {R' : Type u_4} [inst : CommRing R'] [inst_1 : PartialOrder R'] [inst_2 : StarRing R']
[inst_3 : Fintype n] [inst_4 : DecidableEq n] {M : Matrix n n R'}, M.PosSemidef → M⁻¹.PosSemidef- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Matrixstatement and proof · cited by 4,303
- StarRingstatement and proof · cited by 1,686
- IsUnitproof · cited by 1,602
- Matrix.detproof · cited by 665
- Matrix.conjTransposeproof · cited by 202
- Matrix.PosSemidefstatement and proof · cited by 76
- Matrix.conjTranspose_conjTransposeproof · cited by 31
- Matrix.nonsing_inv_apply_not_isUnitproof · cited by 7
- Matrix.PosSemidef.conjTranspose_mul_mul_sameproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.PosSemidef.inv_sqrtproof · cited by 0
- Matrix.PosSemidef.zpowproof · cited by 0