toMatrix_rotation
∀ (a : Circle),
(LinearMap.toMatrix Complex.basisOneI Complex.basisOneI) ↑(rotation a).toLinearEquiv =
↑(Matrix.planeConformalMatrix (↑a).re (↑a).im ⋯)The matrix representation of rotation a is equal to the conformal matrix
!![re a, -im a; im a, re a].
- Defined in
- Mathlib.Analysis.Complex.Isometry
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
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
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- Complexstatement · cited by 5,565
- Matrixstatement · cited by 4,303
- mul_oneproof · cited by 3,885
- MonoidHomstatement · cited by 3,629
- LinearEquivstatement · cited by 3,317
- Submonoidstatement · cited by 3,086
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
Cited by1
Results whose statement or proof uses this declaration.
- det_rotationproof · cited by 1