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Theorems · Definition · group theory

Matrix.GeneralLinearGroup.scalar

(n : Type u) → [inst : DecidableEq n] → [inst_1 : Fintype n] → {R : Type v} → [inst_2 : Semiring R] → Rˣ →* GL n R

Scalar matrix as an element of GL n R.

Defined in
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs
Cited by
18 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqFintypeSemiring

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.GeneralLinearGroup.center_eq_range_scalar · cited by 6GeneralLinearGroup.center…Matrix.GeneralLinearGroup.det_scalar · cited by 3GeneralLinearGroup.det_sc…Matrix.ProjGenLinGroup.lift · cited by 2ProjGenLinGroup.liftUpperHalfPlane.glScalar_smul · cited by 2UpperHalfPlane.glScalar_s…UpperHalfPlane.num_scalar · cited by 1UpperHalfPlane.num_scalarMatrix.ProjGenLinGroup.mk_smul · cited by 1ProjGenLinGroup.mk_smulMatrix.ProjGenLinGroup.mulActionOfGL · cited by 1ProjGenLinGroup.mulAction…UpperHalfPlane.denom_scalar · cited by 1UpperHalfPlane.denom_scal…Matrix.GeneralLinearGroup.map_scalar · cited by 1GeneralLinearGroup.map_sc…Matrix.GeneralLinearGroup.coe_scalar · cited by 1GeneralLinearGroup.coe_sc…Matrix.ProjGenLinGroup.mk_eq_mk_iff · cited by 0ProjGenLinGroup.mk_eq_mk_…Matrix.ProjGenLinGroup.mk_scalar · cited by 0ProjGenLinGroup.mk_scalarMatrix.GeneralLinearGroup.map_center_le · cited by 0GeneralLinearGroup.map_ce…Matrix.ProjectiveSpecialLinearGroup.toPGL_surj_iff · cited by 0ProjectiveSpecialLinearGr…Matrix.GeneralLinearGroup.scalar_commute · cited by 0GeneralLinearGroup.scalar…Semiring · cited by 13802SemiringFintype · cited by 7736FintypeMatrix · cited by 4303MatrixMonoidHom · cited by 3629MonoidHomUnits · cited by 2804UnitsMatrix.GeneralLinearGroup · cited by 556Matrix.GeneralLinearGroupRingHom.toMonoidHom · cited by 132RingHom.toMonoidHomUnits.map · cited by 95Units.mapMatrix.scalar · cited by 62Matrix.scalarGeneralLinearGroup.scalarCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by20

Results whose statement or proof uses this declaration.