Theorems · Theorem · linear algebra
Matrix.PosSemidef.submatrix
∀ {m : Type u_1} {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R]
{M : Matrix n n R}, M.PosSemidef → ∀ (e : m → n), (M.submatrix e e).PosSemidef- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingPartialOrderStarRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Finsuppproof · cited by 5,255
- Matrixstatement and proof · cited by 4,303
- 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.sumproof · cited by 481
- mul_addproof · cited by 413
- add_mulproof · cited by 363
- Matrix.submatrixstatement · cited by 183
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.measurePreserving_restrict₂_multivariateGaussianproof · cited by 1
- Matrix.posSemidef_submatrix_equivproof · cited by 1
- Matrix.PosSemidef.hadamardproof · cited by 0