Theorems · Theorem · linear algebra

Module.Basis.constr_apply

∀ {M' : Type u_7} [inst : AddCommMonoid M'] {ι : Type u_10} {R : Type u_11} {M : Type u_12} [inst_1 : Semiring R]
  [inst_2 : AddCommMonoid M] [inst_3 : Module R M] (b : Module.Basis ι R M) [inst_4 : Module R M'] (S : Type u_13)
  [inst_5 : Semiring S] [inst_6 : Module S M'] [inst_7 : SMulCommClass R S M'] (f : ι → M') (x : M),
  ((b.constr S) f) x = (b.repr x).sum fun b a => a • f b

Defined in

Mathlib.LinearAlgebra.Basis.Defs

Cited by

5 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidSemiringAddCommMonoidModuleModuleSemiringModuleSMulCommClass