Theorems · Theorem · linear algebra
Matrix.PosDef.one
∀ {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], Matrix.PosDef 1- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Matrixstatement · cited by 4,303
- Nontrivialproof · cited by 2,416
- StarRingstatement and proof · cited by 1,686
- StarOrderedRingstatement and proof · cited by 587
- NoZeroDivisorsstatement and proof · cited by 545
- Matrix.PosDefstatement · cited by 68
- zero_lt_one'proof · cited by 16
- Matrix.PosDef.diagonalproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.PosDef.mul_conjTranspose_selfproof · cited by 0
- Matrix.PosDef.conjTranspose_mul_selfproof · cited by 0