Proof of `Symmetric low-rank factorization, including characteristic two` (2nd statement)
groundedproofs/Lax342547Proofs/SymmetricFactorization.lean · lax-342547
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Factor M through its rank and take a left inverse U of the first factor Z. Put H=UMUᵀ. The projection ZU fixes M on the left and, by symmetry, on the right, proving ZHZᵀ=M. The rank of M forces H to be nonsingular.