Theorems · Theorem · linear algebra
Matrix.PosDef.inv
∀ {n : Type u_2} [inst : Fintype n] {K : Type u_5} [inst_1 : Field K] [inst_2 : PartialOrder K] [inst_3 : StarRing K]
[inst_4 : DecidableEq n] {M : Matrix n n K}, M.PosDef → M⁻¹.PosDef- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 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.
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- PartialOrderstatement and proof · cited by 6,410
- Matrixstatement and proof · cited by 4,303
- one_mulproof · cited by 2,841
- StarRingstatement and proof · cited by 1,686
- Invertibleproof · cited by 549
- Matrix.conjTransposeproof · cited by 202
- Matrix.PosDefstatement and proof · cited by 68
- Matrix.conjTranspose_conjTransposeproof · cited by 31
- IsUnit.invertibleproof · cited by 8
- Matrix.inv_mul_of_invertibleproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.posDef_inv_iffproof · cited by 0