Theorems · Theorem · nonassociative algebras

RootPairing.GeckConstruction.h_eq_diagonal

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] {P : RootPairing ι R M N}
  [inst_5 : P.IsCrystallographic] {b : P.Base} [inst_6 : DecidableEq ι] (i : ↥b.support),
  RootPairing.GeckConstruction.h i = Matrix.diagonal (Sum.elim 0 fun x => ↑(P.pairingIn ℤ x ↑i))

Defined in

Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic

Cited by

4 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleRootPairing.IsCrystallographicDecidableEq