Theorems · Theorem · linear algebra
LinearMap.det_toLin
∀ {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] (b : Module.Basis ι R M) (f : Matrix ι ι R),
LinearMap.det ((Matrix.toLin b b) f) = f.det- Defined in
- Mathlib.LinearAlgebra.Determinant
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- MonoidHomstatement · cited by 3,629
- LinearEquivstatement · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- Matrix.detstatement and proof · cited by 665
Cited by5
Results whose statement or proof uses this declaration.
- LinearMap.det_toLin'proof · cited by 4
- det_fderivPolarCoordSymmproof · cited by 3
- associated_norm_prod_smithproof · cited by 1
- Orientation.det_rotationproof · cited by 1
- LinearMap.det_toLpLinproof · cited by 0