Theorems · Theorem · linear algebra
Module.Basis.det_isEmpty
∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {ι : Type u_4}
[inst_3 : DecidableEq ι] [inst_4 : Fintype ι] (e : Module.Basis ι R M) [inst_5 : IsEmpty ι],
e.det = AlternatingMap.constOfIsEmpty R M ι 1- Defined in
- Mathlib.LinearAlgebra.Determinant
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Fintypestatement and proof · cited by 7,736
- Module.Basisstatement and proof · cited by 1,477
- IsEmptystatement and proof · cited by 759
- AlternatingMapstatement · cited by 329
- Module.Basis.detstatement · cited by 73
- AlternatingMap.extproof · cited by 40
- AlternatingMap.constOfIsEmptystatement · cited by 13
- Matrix.det_isEmptyproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Orientation.volumeForm_robustproof · cited by 4
- Orientation.volumeForm_robust'proof · cited by 3
- Module.Basis.orientation_isEmptyproof · cited by 2
- Orientation.volumeForm_robust_negproof · cited by 1