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Eigenvalues of Doubly Stochastic Matrices, an Unfinished Story Mashreghi, Javad
Description
According to a long standing conjecture (sometimes called the Perfect-Mirsky conjecture), the geometric location of eigenvalues of doubly stochastic matrices of order $n$ is exactly the union of all regular $k$-gons with $2 \leq k\leq n$ and anchored at 1 in the closed unit disc. It is easy to verify this fact for $n =2$ and $n=3$. But, for $n\geq 4$, it was an open question at least since 1965. Mashreghi-Rivard (2007) showed that the conjecture is wrong for $n = 5$. Then Levick-Pereira-Kribs (2014) added to the mystery by showing that the conjecture is true for $n=4$. For $n \geq 6$, the loci of eigenvalues is unknown. They also came up with a new formulation of the conjecture.
Item Metadata
Title |
Eigenvalues of Doubly Stochastic Matrices, an Unfinished Story
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-07-08T15:02
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Description |
According to a long standing conjecture (sometimes called the Perfect-Mirsky conjecture), the geometric location of eigenvalues of doubly stochastic matrices of order $n$ is exactly the union of all regular $k$-gons with $2 \leq k\leq n$ and anchored at 1 in the closed unit disc. It is easy to verify this fact for $n =2$ and $n=3$. But, for $n\geq 4$, it was an open question at least since 1965. Mashreghi-Rivard (2007) showed that the conjecture is wrong for $n = 5$. Then Levick-Pereira-Kribs (2014) added to the mystery by showing that the conjecture is true for $n=4$. For $n \geq 6$, the loci of eigenvalues is unknown. They also came up with a new formulation of the conjecture.
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Extent |
31 minutes
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Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Laval University
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Series | |
Date Available |
2018-01-04
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0362591
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International