Theorems · Theorem · number theory

QuadraticMap.basisRepr_apply

∀ {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_8} [inst_5 : Fintype ι] {v : Module.Basis ι R M}
  (Q : QuadraticMap R M N) (w : ι → R), (Q.basisRepr v) w = Q (∑ i, w i • v i)

Defined in: Mathlib.LinearAlgebra.QuadraticForm.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid Module AddCommMonoid Module Fintype

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Cites11

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
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
Fintypestatement and proof · cited by 7,736
Finset.sumstatement · cited by 5,195
Finset.univstatement · cited by 3,473
Module.Basisstatement and proof · cited by 1,477
QuadraticMapstatement and proof · cited by 262
Module.Basis.equivFun_symm_applyproof · cited by 22
QuadraticMap.basisReprstatement and proof · cited by 3

Cited by1

Results whose statement or proof uses this declaration.

QuadraticMap.basisRepr_eq_of_iIsOrthoproof · cited by 0