Theorems · Definition · linear algebra

Finsupp.basis

{R : Type u_1} →
  {M : Type u_2} →
    {ι : Type u_3} →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            {φ : ι → Type u_4} → ((i : ι) → Module.Basis (φ i) R M) → Module.Basis ((i : ι) × φ i) R (ι →₀ M)

The basis on ι →₀ M with basis vectors fun ⟨i, x⟩ ↦ single i (b i x).

Defined in

Mathlib.LinearAlgebra.Finsupp.VectorSpace

Cited by

3 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule