Geodesic
On rank-one corrections of complex symmetric matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 78-83 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let a matrix $A\in M_n(\mathbf C)$ be a rank-one perturbation of a complex symmetric matrix, i.e. $A=X+Y$ for some unknown matrices $X$ and $Y$ such that $X=X^T$ and $\mathrm{rank}\,Y=1$. The problem of determining the matrices $X$ and $Y$ is solved. 
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M. Dana; Kh. D. Ikramov. On rank-one corrections of complex symmetric matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 78-83. http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a5/

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