Theorems · Theorem · linear algebra
Matrix.posSemidef_gram
∀ {E : Type u_1} {n : Type u_2} (𝕜 : Type u_4) [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E]
[inst_2 : InnerProductSpace 𝕜 E] [Finite n] (v : n → E), (Matrix.gram 𝕜 v).PosSemidefA Gram matrix is positive semidefinite.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fintypeproof · cited by 7,736
- Norm.normproof · cited by 5,413
- Finset.sumproof · cited by 5,195
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univproof · cited by 3,473
- Finitestatement and proof · cited by 3,029
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- map_zeroproof · cited by 1,614
- RCLike.reproof · cited by 319
- Fintype.ofFiniteproof · cited by 255
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.posSemidef_matrix_measure_interproof · cited by 1
- Matrix.posDef_gram_of_linearIndependentproof · cited by 1
- Matrix.linearIndependent_of_det_gram_ne_zeroproof · cited by 1
- Matrix.det_gram_ne_zero_iff_linearIndependentproof · cited by 0