Theorems · Definition · linear algebra

Fintype.bilinearCombination

{α : Type u_1} →
  {M : Type u_2} →
    (R : Type u_3) →
      [Fintype α] →
        [inst : Semiring R] →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : Module R M] →
              (S : Type u_4) →
                [inst_3 : Semiring S] →
                  [inst_4 : Module S M] → [inst_5 : SMulCommClass R S M] → (α → M) →ₗ[S] (α → R) →ₗ[R] M

Fintype.bilinearCombination R S v f is the linear combination of vectors in v with weights in f. This variant of Finsupp.linearCombination is defined on fintype indexed vectors. This map is linear in v if R is commutative, and always linear in f. See note [bundled maps over different rings] for why separate R and S semirings are used.

Defined in

Mathlib.LinearAlgebra.Finsupp.LinearCombination

Cited by

2 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeSemiringAddCommMonoidModuleSemiringModuleSMulCommClass