Short proofs of theorems of mirsky and horn on diagonals and eigenvalues of matrices

Eric A. Carlen; Elliott H. Lieb

doi:10.13001/1081-3810.1323

Short proofs of theorems of mirsky and horn on diagonals and eigenvalues of matrices

Eric A. Carlen
, Elliott H. Lieb

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English (US)
Pages (from-to)	438-441
Number of pages	4
Journal	Electronic Journal of Linear Algebra
Volume	18
DOIs	https://doi.org/10.13001/1081-3810.1323
State	Published - 2009

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Eigenvalues
Majorization
Prescribed diagonals

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10.13001/1081-3810.1323

Cite this

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title = "Short proofs of theorems of mirsky and horn on diagonals and eigenvalues of matrices",

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.",

keywords = "Eigenvalues, Majorization, Prescribed diagonals",

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year = "2009",

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language = "English (US)",

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pages = "438--441",

journal = "Electronic Journal of Linear Algebra",

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T1 - Short proofs of theorems of mirsky and horn on diagonals and eigenvalues of matrices

AU - Carlen, Eric A.

AU - Lieb, Elliott H.

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N2 - 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.

AB - 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.

KW - Eigenvalues

KW - Majorization

KW - Prescribed diagonals

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UR - https://www.scopus.com/pages/publications/70349437128#tab=citedBy

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DO - 10.13001/1081-3810.1323

M3 - Article

AN - SCOPUS:70349437128

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VL - 18

SP - 438

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JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

ER -

Short proofs of theorems of mirsky and horn on diagonals and eigenvalues of matrices

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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