Geodesic
Matrices with Prescribed Principal Elements and Singular Values
Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 247-249

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We shall be concerned with the following problem. Let a11, ..., ann be complex numbers and λ1, ..., λn nonnegative real numbers. Under what conditions does there exist an n × n complex matrix A with a 11, ..., ann as principal elements and λ1, ..., λn as singular values? This problem has been suggested in [3] but, to our knowledge, has not yet been solved. 
Oliveira, Graciano N. De. Matrices with Prescribed Principal Elements and Singular Values. Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 247-249. doi: 10.4153/CMB-1971-043-4
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     title = {Matrices with {Prescribed} {Principal} {Elements} and {Singular} {Values}},
     journal = {Canadian mathematical bulletin},
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     year = {1971},
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     number = {2},
     doi = {10.4153/CMB-1971-043-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-043-4/}
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