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

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

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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[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. Mirsky, L., Matrices with prescribed characteristic roots and diagonal elements, J. London Math. Soc. 33 (1958), 14-21. Google Scholar

[3] 3. Mirsky, L., Inequalities and existence theorems in the theory of matrices, J. Math. Anal. Appl. 9(1964), 99-118. Google Scholar

[4] 4. Thompson, R. C., Principal submatrices IX: Interlacing inequalities for singular values of submatrices, Linear Algebra and its Applications (to appear). Google Scholar

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