Geodesic
Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices
The electronic journal of linear algebra, Tome 18 (2009), pp. 438-441.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N-square complex matrix with prescribed diagonal entries and prescribed eigenvalues. A simple inductive proof of this theorem is given.
Classification : 15A42, 15A51
Keywords: majorization, eigenvalues, prescribed diagonals 
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     author = {Carlen, Eric A. and Lieb, Elliott H.},
     title = {Short proofs of theorems of {Mirsky} and {Horn} on diagonals and eigenvalues of matrices},
     journal = {The electronic journal of linear algebra},
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Carlen, Eric A.; Lieb, Elliott H. Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices. The electronic journal of linear algebra, Tome 18 (2009), pp. 438-441. http://geodesic.mathdoc.fr/item/ELA_2009__18__a23/