Theorems · Theorem · number theory
LinearMap.BilinForm.toQuadraticMap_isOrtho
∀ {R : Type u_3} {M : Type u_4} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [IsCancelAdd R]
[NoZeroDivisors R] [CharZero R] {B : LinearMap.BilinMap R M R} {x y : M},
LinearMap.IsSymm B → (B.toQuadraticMap.IsOrtho x y ↔ (B x) y = 0)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Quot.sound
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- add_commproof · cited by 1,535
- map_addproof · cited by 964
- CharZerostatement and proof · cited by 932
- NoZeroDivisorsstatement and proof · cited by 545
- LinearMap.BilinMapstatement and proof · cited by 85
- IsCancelAddstatement and proof · cited by 79
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