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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Horn, A., On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. Math. Soc. 5 (1954), 4–7. Google Scholar

[2] 2. Horn, A., Doubly stochastic matrices and diagonal of a rotation matrix, Amer. J. of Math. 76(1954)620–630. Google Scholar

[3] 3. Mirsky, L., On a convex set of matrices, Arch. Math. Vol. 10 (1959), 88–92. Google Scholar

[4] 4. De Oliviera, G. N. , Matrices with prescribed principal elements and singular values, Canad. Math. Bull. 14 (2), 1971, 247–249. Google Scholar

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