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Theorems · Theorem · number theory

QuadraticMap.map_smul

∀ {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] (Q : QuadraticMap R M N) (a : R) (x : M), Q (a • x) = (a * a) • Q x
Defined in
Mathlib.LinearAlgebra.QuadraticForm.Basic
Cited by
11 results in Mathlib
Foundations
Depth 38 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringAddCommMonoidModuleAddCommMonoidModule
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

QuadraticMap.polar_smul_left · cited by 5QuadraticMap.polar_smul_l…QuadraticMap.radical_eq_ker_polarBilin · cited by 3QuadraticMap.radical_eq_k…QuadraticMap.hasLineDerivAt · cited by 2QuadraticMap.hasLineDeriv…QuadraticMap.map_add_self · cited by 2QuadraticMap.map_add_selfbaseChange_ext · cited by 2baseChange_extQuadraticMap.map_zero · cited by 2QuadraticMap.map_zeroQuadraticMap.toQuadraticMap_toBilin · cited by 1QuadraticMap.toQuadraticM…QuadraticMap.map_neg · cited by 1QuadraticMap.map_negQuadraticMap.apply_linearCombination · cited by 1QuadraticMap.apply_linear…QuadraticMap.apply_linearCombination' · cited by 1QuadraticMap.apply_linear…QuadraticMap.map_smul_of_tower · cited by 0QuadraticMap.map_smul_of_…DFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringQuadraticMap · cited by 262QuadraticMapQuadraticMap.toFun_smul · cited by 1QuadraticMap.toFun_smulQuadraticMap.map_smulCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by11

Results whose statement or proof uses this declaration.