= Analytic determinant square root for accretive symmetric matrices
{title2=$d(A)=\exp[\tfrac12\operatorname{tr}\operatorname{Log}A]$}
On complex symmetric <matrices> with positive-definite real part, the <determinant> has a nonzero analytic square root normalized positively on real positive <matrices>. It is continued within this accretive domain. For $A=G+iB$, put $C=G^{-1/2}BG^{-1/2}$ with real <eigenvalues> $b_j$; then $d(A)=\sqrt{\det G}\prod_j\sqrt{1+ib_j}$, using positive-real-part roots for each factor. The principal scalar square root of the product <determinant> need not equal this continued root: accumulated <determinant> arguments can cross the scalar branch cut. The principal <matrix> logarithm instead tracks all factors consistently.
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