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[^Bunch1977]: J R Bunch and L Kaufman, Some stable methods for calculating inertia and solving symmetric linear systems, Mathematics of Computation 31:137 (1977), 163-179. [url](http://www.ams.org/journals/mcom/1977-31-137/S0025-5718-1977-0428694-0).
# 2x2 pivot case. Make sure not to square before the subtraction by scaling with the off-diagonal element. This is safe because the off diagonal is always large for 2x2 pivots.
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if F.uplo =='U'
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d *= M[i, i +1]*(M[i,i]/M[i, i +1]*M[i +1, i +1] - (issym(F) ? M[i, i +1] :conj(M[i, i +1])))
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d *= M[i, i +1]*(M[i,i]/M[i, i +1]*M[i +1, i +1] - (issymmetric(F) ? M[i, i +1] :conj(M[i, i +1])))
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else
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d *= M[i +1,i]*(M[i, i]/M[i +1, i]*M[i +1, i +1] - (issym(F) ? M[i +1, i] :conj(M[i +1, i])))
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d *= M[i +1,i]*(M[i, i]/M[i +1, i]*M[i +1, i +1] - (issymmetric(F) ? M[i +1, i] :conj(M[i +1, i])))
Copy file name to clipboardexpand all lines: doc/stdlib/linalg.rst
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@@ -423,7 +423,7 @@ Linear algebra functions in Julia are largely implemented by calling functions f
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.. Docstring generated from Julia source
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Compute the Bunch-Kaufman [Bunch1977]_ factorization of a real symmetric or complex Hermitian matrix ``A`` and return a ``BunchKaufman`` object. The following functions are available for ``BunchKaufman`` objects: ``size``\ , ``\``\ , ``inv``\ , ``issym``\ , ``ishermitian``\ .
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Compute the Bunch-Kaufman [Bunch1977]_ factorization of a real symmetric or complex Hermitian matrix ``A`` and return a ``BunchKaufman`` object. The following functions are available for ``BunchKaufman`` objects: ``size``\ , ``\``\ , ``inv``\ , ``issymmetric``\ , ``ishermitian``\ .
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.. [Bunch1977] J R Bunch and L Kaufman, Some stable methods for calculating inertia and solving symmetric linear systems, Mathematics of Computation 31:137 (1977), 163-179. `url <http://www.ams.org/journals/mcom/1977-31-137/S0025-5718-1977-0428694-0>`_\ .
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@@ -1093,7 +1093,7 @@ Linear algebra functions in Julia are largely implemented by calling functions f
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Computes the solution ``X`` to the Sylvester equation ``AX + XB + C = 0``\ , where ``A``\ , ``B`` and ``C`` have compatible dimensions and ``A`` and ``-B`` have no eigenvalues with equal real part.
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