Short Proofs of Theorems of Mirsky and Horn on Diagonals and Eigenvalues of Matrices
E. Carlen, and E. Lieb. 18, page 438-441. Pensacola, Fla, International Linear Algebra Society., (July 2009)
Abstract
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.
%0 Conference Paper
%1 carlen2009short
%A Carlen, Eric A.
%A Lieb, Elliott H.
%C Pensacola, Fla
%D 2009
%I International Linear Algebra Society.
%J The electronic journal of linear algebra
%K majorization matrix
%P 438-441
%T Short Proofs of Theorems of Mirsky and Horn on Diagonals and Eigenvalues of Matrices
%U http://hermite.cii.fc.ul.pt/iic/ela/ela-articles/articles/vol18_pp438-441.pdf
%V 18
%X 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.
@inproceedings{carlen2009short,
abstract = {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.},
added-at = {2013-12-21T20:46:00.000+0100},
address = {Pensacola, Fla},
author = {Carlen, Eric A. and Lieb, Elliott H.},
biburl = {https://www.bibsonomy.org/bibtex/22f6020f8385fe7d7f32a048b792e8f1b/ytyoun},
interhash = {0df7591ce6a34616bee281d23481b745},
intrahash = {2f6020f8385fe7d7f32a048b792e8f1b},
journal = {The electronic journal of linear algebra},
keywords = {majorization matrix},
month = {July},
pages = {438-441},
publisher = {International Linear Algebra Society.},
timestamp = {2013-12-23T01:38:26.000+0100},
title = {Short Proofs of Theorems of Mirsky and Horn on Diagonals and Eigenvalues of Matrices},
url = {http://hermite.cii.fc.ul.pt/iic/ela/ela-articles/articles/vol18_pp438-441.pdf},
volume = 18,
year = 2009
}