Theorems · Definition · nonassociative algebras
LieAlgebra.Orthogonal.PD
(l : Type u_4) → (R : Type u₂) → [DecidableEq l] → [CommRing R] → Matrix (l ⊕ l) (l ⊕ l) R
A matrix transforming the bilinear form defined by the matrix JD into a split-signature
diagonal matrix.
It looks like this as a 2l x 2l matrix of l x l blocks:
``
[ 1 -1 ]
[ 1 1 ]
``
- Defined in
- Mathlib.Algebra.Lie.Classical
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Quot.sound
- Assumes
- DecidableEqCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Matrixstatement · cited by 4,303
- Matrix.fromBlocksproof · cited by 108
Cited by7
Results whose statement or proof uses this declaration.
- LieAlgebra.Orthogonal.PBproof · cited by 2
- LieAlgebra.Orthogonal.jd_transformstatement and proof · cited by 1
- LieAlgebra.Orthogonal.typeDEquivSo'proof · cited by 0
- LieAlgebra.Orthogonal.PD.congr_simpstatement and proof · cited by 0
- LieAlgebra.Orthogonal.jb_transformproof · cited by 0
- LieAlgebra.Orthogonal.pb_invstatement and proof · cited by 0
- LieAlgebra.Orthogonal.pd_invstatement · cited by 0