Theorems · Theorem · number theory

LinearMap.BilinMap.toQuadraticMap_sum

∀ {R : Type u_3} {M : Type u_4} {N : Type u_5} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N] {ι : Type u_9} (s : Finset ι) (B : ι → LinearMap.BilinMap R M N),
  (∑ i ∈ s, B i).toQuadraticMap = ∑ i ∈ s, (B i).toQuadraticMap

Defined in: Mathlib.LinearAlgebra.QuadraticForm.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 47 from the axioms · uses propext, Quot.sound
Assumes: CommSemiring AddCommMonoid Module AddCommMonoid Module

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Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
Finsetstatement and proof · cited by 13,712
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
LinearMapstatement · cited by 10,215
Finset.sumstatement · cited by 5,195
map_sumproof · cited by 455
QuadraticMapstatement · cited by 262
LinearMap.BilinMapstatement and proof · cited by 85
LinearMap.BilinMap.toQuadraticMapstatement · cited by 53
LinearMap.BilinMap.toQuadraticMapAddMonoidHomproof · cited by 4

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