Geodesic
Some Results on Matrices with Prescribed Diagonal Elements and Singular Values
Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 89-92

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Let A be an n × n complex matrix. The singular values of A are the non-negative square-roots of the eigenvalues of A*A. G. N. De Oliviera [4] gave a necessary condition for the existence of a matrix A with a 1..., a n as diagonal elements and α1,..., αn as singular values. We shall give another necessary condition which implies the above author’s condition and we show that this is also a sufficient condition for the case n =2. 
Sing, Fuk-Yum. Some Results on Matrices with Prescribed Diagonal Elements and Singular Values. Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 89-92. doi: 10.4153/CMB-1976-012-5
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     title = {Some {Results} on {Matrices} with {Prescribed} {Diagonal} {Elements} and {Singular} {Values}},
     journal = {Canadian mathematical bulletin},
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     year = {1976},
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     doi = {10.4153/CMB-1976-012-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-012-5/}
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