#12966: Indefinite factorization for exact matrices
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Reporter: rbeezer | Owner: jason, was
Type: enhancement | Status: new
Priority: minor | Milestone: sage-5.1
Component: linear algebra | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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Almost any square symmetric (or Hermitian) matrix A over a field can be
decomposed into a lower triangular matrix L and a diagonal matrix D such
that A = L*D*L-transpose, suitably adjusted in the Hermitian case.
1) This is of interest for its own sake (eg for solving systems).
2) If the field has square roots and the diagonal matrix has positive
entries, then the Cholesky decomposition is easy. This would fix #11274.
3) This will give a good way to tell if a matrix is positive definite.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12966>
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