Theorems · Theorem · linear algebra
LinearMap.det_ring
∀ {R : Type u_1} [inst : CommRing R] (f : R →ₗ[R] R), LinearMap.det f = f 1When the function is over the base ring, the determinant is the evaluation at 1.
- Defined in
- Mathlib.LinearAlgebra.Determinant
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement and proof · cited by 10,215
- MonoidHomstatement · cited by 3,629
- LinearMap.toMatrixproof · cited by 180
- LinearMap.detstatement · cited by 127
- LinearMap.det_toMatrixproof · cited by 37
- Matrix.det_uniqueproof · cited by 15
- Module.Basis.singletonproof · cited by 15
- LinearMap.toMatrix_singletonproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- Algebra.norm_selfproof · cited by 6
- MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_monotoneOnproof · cited by 3
- MeasureTheory.integral_image_eq_integral_deriv_smul_of_monotoneOnproof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasisproof · cited by 1
- ContinuousLinearMap.det_smulRightproof · cited by 1
- LinearMap.det_mulLeftproof · cited by 0
- LinearMap.det_mulRightproof · cited by 0
- UpperHalfPlane.det_smulFDerivproof · cited by 0