Principal Minor Sums of (A+tB)m

Peter McNamara; Charles R. Johnson; Stefan Leichenauer; Roberto Costas

Principal Minor Sums of (A+tB)m

Peter McNamara
, Charles R. Johnson
, Stefan Leichenauer
, Roberto Costas

Bucknell University

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

Abstract

The question is raised whether the sum of the k -by- k principal minors of the titled matrix is a polynomial (in t ) with positive coefficients, when A and B are positive-definite. This would generalize a conjecture made by Bessis-Moussa-Villani, as stated by Lieb and Seiringer. We give a variety of evidence for this further question, some of which is new.

Original language	American English
Journal	Default journal
Volume	411
State	Published - Jan 1 2005

Disciplines

Mathematics

Access to Document

http://www.facstaff.bucknell.edu/pm040/Papers/minorsums2.pdf

Cite this

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title = "Principal Minor Sums of (A+tB)m",

abstract = " The question is raised whether the sum of the k -by- k principal minors of the titled matrix is a polynomial (in t ) with positive coefficients, when A and B are positive-definite. This would generalize a conjecture made by Bessis-Moussa-Villani, as stated by Lieb and Seiringer. We give a variety of evidence for this further question, some of which is new.",

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AU - McNamara, Peter

AU - Johnson, Charles R.

AU - Leichenauer, Stefan

AU - Costas, Roberto

PY - 2005/1/1

Y1 - 2005/1/1

N2 - The question is raised whether the sum of the k -by- k principal minors of the titled matrix is a polynomial (in t ) with positive coefficients, when A and B are positive-definite. This would generalize a conjecture made by Bessis-Moussa-Villani, as stated by Lieb and Seiringer. We give a variety of evidence for this further question, some of which is new.

AB - The question is raised whether the sum of the k -by- k principal minors of the titled matrix is a polynomial (in t ) with positive coefficients, when A and B are positive-definite. This would generalize a conjecture made by Bessis-Moussa-Villani, as stated by Lieb and Seiringer. We give a variety of evidence for this further question, some of which is new.

UR - https://digitalcommons.bucknell.edu/fac_journ/109

UR - http://www.facstaff.bucknell.edu/pm040/Papers/minorsums2.pdf

M3 - Article

VL - 411

JO - Default journal

JF - Default journal

ER -

Principal Minor Sums of (A+tB)m

Abstract

Disciplines

Access to Document

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Cite this