On the spectral radius of the product of matrix exponentials

Elliott H. Lieb

doi:10.1016/0024-3795(90)90324-6

On the spectral radius of the product of matrix exponentials

Elliott H. Lieb

Mathematics

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Abstract

Cohen, Friedland, Kato, and Kelly conjectured that F(t)≡log r(e^Ate^Bt) is convex for real t when A is nonnegative and B is diagonal; here r is the spectral radius. While the conjecture is correct for dimension n=1 or 2, it is shown here to be false for n≥3. Similarly t → logTrace(e^Ate^Bt)k need not be convex when n≥3.

Original language	English (US)
Pages (from-to)	271-273
Number of pages	3
Journal	Linear Algebra and Its Applications
Volume	141
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(90)90324-6
State	Published - Nov 1990

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/0024-3795(90)90324-6

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title = "On the spectral radius of the product of matrix exponentials",

abstract = "Cohen, Friedland, Kato, and Kelly conjectured that F(t)≡log r(eAteBt) is convex for real t when A is nonnegative and B is diagonal; here r is the spectral radius. While the conjecture is correct for dimension n=1 or 2, it is shown here to be false for n≥3. Similarly t → logTrace(eAteBt)k need not be convex when n≥3.",

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N2 - Cohen, Friedland, Kato, and Kelly conjectured that F(t)≡log r(eAteBt) is convex for real t when A is nonnegative and B is diagonal; here r is the spectral radius. While the conjecture is correct for dimension n=1 or 2, it is shown here to be false for n≥3. Similarly t → logTrace(eAteBt)k need not be convex when n≥3.

AB - Cohen, Friedland, Kato, and Kelly conjectured that F(t)≡log r(eAteBt) is convex for real t when A is nonnegative and B is diagonal; here r is the spectral radius. While the conjecture is correct for dimension n=1 or 2, it is shown here to be false for n≥3. Similarly t → logTrace(eAteBt)k need not be convex when n≥3.

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U2 - 10.1016/0024-3795(90)90324-6

DO - 10.1016/0024-3795(90)90324-6

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EP - 273

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

On the spectral radius of the product of matrix exponentials

Abstract

All Science Journal Classification (ASJC) codes

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