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If the matrix is symmetric indefinite, it may be still decomposed as <math>PAP^\textsf{T} = LDL^\textsf{T}</math> where <math>P</math> is a permutation matrix (arising from the need to [[pivot element|pivot]]), <math>L</math> a lower unit triangular matrix, and <math>D</math> {{Relevance inline|reason=not referred to in this section|date=December 2015}} is a direct sum of symmetric <math>1 \times 1</math> and <math>2 \times 2</math> blocks, which is called Bunch–Kaufman decomposition <ref>{{cite book | author=G.H. Golub, C.F. van Loan. | title=Matrix Computations | publisher=The Johns Hopkins University Press, Baltimore, London | year=1996}}</ref>
A complex symmetric matrix may be [[defective matrix|defective]] and thus not be diagonalizable. If a complex symmetric matrix
:<math>A = Q \Lambda Q^\textsf{T}</math>
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