Theorems · Definition · linear algebra

Module.Basis.reindexFinsetRange

{ι : Type u_10} →
  {R : Type u_11} →
    {M : Type u_12} →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            (b : Module.Basis ι R M) →
              [inst_3 : Fintype ι] → [inst_4 : DecidableEq M] → Module.Basis (↥(Finset.image (⇑b) Finset.univ)) R M

b.reindexFinsetRange is a basis indexed by Finset.univ.image b, the finite set of basis vectors themselves.

Defined in

Mathlib.LinearAlgebra.Basis.Defs

Cited by

7 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleFintypeDecidableEq