Theorems · Theorem · linear algebra
LinearEquiv.det_coe_symm
∀ {M : Type u_2} [inst : AddCommGroup M] {𝕜 : Type u_5} [inst_1 : Field 𝕜] [inst_2 : Module 𝕜 M] (f : M ≃ₗ[𝕜] M),
LinearMap.det ↑f.symm = (LinearMap.det ↑f)⁻¹The determinant of f.symm is the inverse of that of f when f is a linear equiv.
- Defined in
- Mathlib.LinearAlgebra.Determinant
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupFieldModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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 and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- MonoidHomstatement · cited by 3,629
- LinearEquivstatement and proof · cited by 3,317
- one_mulproof · cited by 2,841
- LinearEquiv.symmstatement and proof · cited by 1,461
- LinearEquiv.toLinearMapstatement and proof · cited by 1,171
- one_ne_zeroproof · cited by 885
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaar_preimage_linearEquivproof · cited by 3
- ContinuousLinearEquiv.det_coe_symmproof · cited by 1