Convex trace functions of several variables

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Standard

Convex trace functions of several variables. / Hansen, Frank.

I: Linear Algebra and Its Applications, Bind 341, Nr. 1-3, 2002, s. 309-315.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Hansen, F 2002, 'Convex trace functions of several variables', Linear Algebra and Its Applications, bind 341, nr. 1-3, s. 309-315. https://doi.org/10.1016/S0024-3795(01)00392-5

APA

Hansen, F. (2002). Convex trace functions of several variables. Linear Algebra and Its Applications, 341(1-3), 309-315. https://doi.org/10.1016/S0024-3795(01)00392-5

Vancouver

Hansen F. Convex trace functions of several variables. Linear Algebra and Its Applications. 2002;341(1-3):309-315. https://doi.org/10.1016/S0024-3795(01)00392-5

Author

Hansen, Frank. / Convex trace functions of several variables. I: Linear Algebra and Its Applications. 2002 ; Bind 341, Nr. 1-3. s. 309-315.

Bibtex

@article{790a3aa0ad3f11dbbee902004c4f4f50,
title = "Convex trace functions of several variables",
abstract = "We prove that the function (x1,...,xk)¿Tr(f(x1,...,xk)), defined on k-tuples of symmetric matrices of order (n1,...,nk) in the domain of f, is convex for any convex function f of k variables. The matrix f(x1,...,xk) is defined by the functional calculus for functions of several variables, and it is symmetric and of order n1,...,nk. ",
author = "Frank Hansen",
note = "JEL Classification: C00",
year = "2002",
doi = "10.1016/S0024-3795(01)00392-5",
language = "English",
volume = "341",
pages = "309--315",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
publisher = "Elsevier",
number = "1-3",

}

RIS

TY - JOUR

T1 - Convex trace functions of several variables

AU - Hansen, Frank

N1 - JEL Classification: C00

PY - 2002

Y1 - 2002

N2 - We prove that the function (x1,...,xk)¿Tr(f(x1,...,xk)), defined on k-tuples of symmetric matrices of order (n1,...,nk) in the domain of f, is convex for any convex function f of k variables. The matrix f(x1,...,xk) is defined by the functional calculus for functions of several variables, and it is symmetric and of order n1,...,nk.

AB - We prove that the function (x1,...,xk)¿Tr(f(x1,...,xk)), defined on k-tuples of symmetric matrices of order (n1,...,nk) in the domain of f, is convex for any convex function f of k variables. The matrix f(x1,...,xk) is defined by the functional calculus for functions of several variables, and it is symmetric and of order n1,...,nk.

U2 - 10.1016/S0024-3795(01)00392-5

DO - 10.1016/S0024-3795(01)00392-5

M3 - Journal article

VL - 341

SP - 309

EP - 315

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1-3

ER -

ID: 138627