Geodesic
The strengthened versions of the additive and multiplicative Weyl inequalities
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 39-59 
L. Yu. Kolotilina. The strengthened versions of the additive and multiplicative Weyl inequalities. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 39-59. http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a3/
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     author = {L. Yu. Kolotilina},
     title = {The strengthened versions of the additive and multiplicative {Weyl} inequalities},
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     pages = {39--59},
     year = {2003},
     volume = {296},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a3/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The strengthened versions of the classical additive and multiplicative Weyl inequalities for the singular values of $A+B$ and $AB^*$, where $A$ and $B$ are rectangular matrices, and for the eigenvalues of $A+B$ and $AB$, where $A$ and $B$ are Hermitian matrices, are established under certain assumptions on the subspaces spanned by some singular vectors or eigenvectors of $A$ and $B$.

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