Some factorizations of matrix functions in several variables

Jaromír Šimša

Archivum Mathematicum (1992)

  • Volume: 028, Issue: 1-2, page 85-94
  • ISSN: 0044-8753

Abstract

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We establish some criteria for a nonsingular square matrix depending on several parameters to be represented in the form of a matrix product of factors which depend on the single parameters.

How to cite

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Šimša, Jaromír. "Some factorizations of matrix functions in several variables." Archivum Mathematicum 028.1-2 (1992): 85-94. <http://eudml.org/doc/247352>.

@article{Šimša1992,
abstract = {We establish some criteria for a nonsingular square matrix depending on several parameters to be represented in the form of a matrix product of factors which depend on the single parameters.},
author = {Šimša, Jaromír},
journal = {Archivum Mathematicum},
keywords = {separation of variables; matrix-valued functions; functional and differential equations for factorizable functions; factorizable matrix-valued functions; differentiable; partial derivatives; Wronski equations; counter-examples},
language = {eng},
number = {1-2},
pages = {85-94},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some factorizations of matrix functions in several variables},
url = {http://eudml.org/doc/247352},
volume = {028},
year = {1992},
}

TY - JOUR
AU - Šimša, Jaromír
TI - Some factorizations of matrix functions in several variables
JO - Archivum Mathematicum
PY - 1992
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 028
IS - 1-2
SP - 85
EP - 94
AB - We establish some criteria for a nonsingular square matrix depending on several parameters to be represented in the form of a matrix product of factors which depend on the single parameters.
LA - eng
KW - separation of variables; matrix-valued functions; functional and differential equations for factorizable functions; factorizable matrix-valued functions; differentiable; partial derivatives; Wronski equations; counter-examples
UR - http://eudml.org/doc/247352
ER -

References

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  1. Recherches sur la courbe que forme une corde tendue mise en vibration I – II, Hist. Acad. Berlin (1747), 214-249. (1747) 
  2. Decomposable functions of several variables, Aequationes Math. 40 (1990), 8-25. (1990) MR1055187
  3. Decomposition of smooth functions of two multidimensional variables, Czechoslovak Math. J. 41(116) (1991), 342-358. (1991) MR1105450
  4. Sums of products of functions of x times functions of y , Linear Algebra Appl. 125 (1989), 19-63. (1989) MR1024482
  5. Factorizations of matrices and functions of two variables, Czechoslovak Math. J. 32(107) (1982), 582-588. (1982) Zbl0517.15012MR0682133
  6. Finite sums of products of functions in single variables, Linear Algebra Appl. 134 (1990), 153-164. (1990) Zbl0714.26007MR1060018
  7. Functions decomposable into finite sums of products, in “Constantin Carathéodory: An International Tribute”, World Scientific Publ. Co., 1991, pp. 956-963. (1991) MR1130873
  8. A criterion for a function to be represented as a sum of products of factors, Bull. Inst. Math. Acad. Sinica 14 (1986), 377-382. (1986) Zbl0643.26009MR0885367
  9. Sur une categorie d’équations fonctionelles, in Rend. Circ. Mat. Palermo 18 (1904), 360-362. (1904) 

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