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Theorems · Theorem · nonassociative algebras

Matrix.isSimplyLaced_iff_of_linearOrder

∀ {ι : Type u_1} [inst : LinearOrder ι] (A : Matrix ι ι ℤ),
  A.IsSymm → (A.IsSimplyLaced ↔ ∀ ⦃i j : ι⦄, j < i → A i j = 0 ∨ A i j = -1)
Defined in
Mathlib.LinearAlgebra.Matrix.Cartan
Cited by
3 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Quot.sound
Assumes
LinearOrder
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Around this declaration

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

CartanMatrix.isSimplyLaced_E₆ · cited by 0CartanMatrix.isSimplyLace…CartanMatrix.isSimplyLaced_E₇ · cited by 0CartanMatrix.isSimplyLace…CartanMatrix.isSimplyLaced_E₈ · cited by 0CartanMatrix.isSimplyLace…LinearOrder · cited by 8572LinearOrderMatrix · cited by 4303MatrixLT.lt.ne' · cited by 1417lt.ne'Ne.lt_or_gt · cited by 108Ne.lt_or_gtMatrix.IsSymm · cited by 70Matrix.IsSymmMatrix.IsSimplyLaced · cited by 9Matrix.IsSimplyLacedMatrix.IsSymm.apply · cited by 4IsSymm.applyMatrix.isSimplyLaced_iff_of_l…CITED BYCITES

Cites7

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Cited by3

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