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Singular Cholesky Fibers over Finite Fields
For a finite field $\F_q$, consider the triangular Cholesky map $Γ_{n,q}(U)=U^TU$ from upper triangular matrices to symmetric matrices. Generalized Cholesky theory describes the regular locus on which all leading principal minors are nonzero, but it does not determine the multiplicities or root rank
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