Theorems · Definition · linear algebra

Module.Basis.adjustToOrientation

{R : Type u_1} →
  [inst : CommRing R] →
    [inst_1 : LinearOrder R] →
      [inst_2 : IsStrictOrderedRing R] →
        {M : Type u_2} →
          [inst_3 : AddCommGroup M] →
            [inst_4 : Module R M] →
              {ι : Type u_3} →
                [Fintype ι] →
                  [DecidableEq ι] → [Nonempty ι] → Module.Basis ι R M → Orientation R M ι → Module.Basis ι R M

Given a basis and an orientation, return a basis giving that orientation: either the original basis, or one constructed by negating a single (arbitrary) basis vector.

Defined in

Mathlib.LinearAlgebra.Orientation

Cited by

7 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLinearOrderIsStrictOrderedRingAddCommGroupModuleFintypeDecidableEqNonempty