Some remarks on unilateral matrix equations

Cerchiai, Bianca L; Zumino, Bruno

Title: Some remarks on unilateral matrix equations

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Abstract

We briefly review the results of our paper LBNL-46775: We study certain solutions of left-unilateral matrix equations. These are algebraic equations where the coefficients and the unknown are square matrices of the same order, or, more abstractly, elements of an associative, but possibly noncommutative algebra, and all coefficients are on the left. Recently such equations have appeared in a discussion of generalized Born-Infeld theories. In particular, two equations, their perturbative solutions and the relation between them are studied, applying a unified approach based on the generalized Bezout theorem for matrix polynomials.

Authors:: Cerchiai, Bianca L; Zumino, Bruno

Publication Date:: Thu Feb 01 00:00:00 EST 2001

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Director, Office of Science. Office of High Energy and Nuclear Physics. Division of High Energy Physics; DEUTSCHE FORSCHUNGSGEMEINSCHAFT GRANT CE 50/1-1 (US)

OSTI Identifier:: 783765

Report Number(s):: LBNL-47482
R&D Project: 417001; TRN: US0104077

DOE Contract Number:: AC03-76SF00098

Resource Type:: Conference

Resource Relation:: Conference: Euroconference 'Brane New World and Noncommutative Geometry, Torino (IT), 10/02/2000--10/07/2000; Other Information: PBD: 1 Feb 2001

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGEBRA; GEOMETRY; MATRICES; POLYNOMIALS; EQUATIONS; BORN-INFELD THEORY; UNILATERAL MATRIX EQUATIONS

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                    Cerchiai, Bianca L, and Zumino, Bruno. Some remarks on unilateral matrix equations.  United States: N. p., 2001. 
        Web.

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                    Cerchiai, Bianca L, & Zumino, Bruno. Some remarks on unilateral matrix equations.  United States.

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                    Cerchiai, Bianca L, and Zumino, Bruno. 2001.  
        "Some remarks on unilateral matrix equations".  United States.  https://www.osti.gov/servlets/purl/783765.

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@article{osti_783765,

  title        = {Some remarks on unilateral matrix equations},

  author       = {Cerchiai, Bianca L and Zumino, Bruno},

  abstractNote = {We briefly review the results of our paper LBNL-46775: We study certain solutions of left-unilateral matrix equations. These are algebraic equations where the coefficients and the unknown are square matrices of the same order, or, more abstractly, elements of an associative, but possibly noncommutative algebra, and all coefficients are on the left. Recently such equations have appeared in a discussion of generalized Born-Infeld theories. In particular, two equations, their perturbative solutions and the relation between them are studied, applying a unified approach based on the generalized Bezout theorem for matrix polynomials.},

  doi          = {},

  url          = {https://www.osti.gov/biblio/783765},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Thu Feb 01 00:00:00 EST 2001},

  month        = {Thu Feb 01 00:00:00 EST 2001}

}

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Some remarks on unilateral matrix equations

Conference Cerchiai, Bianca; Zumino, Bruno

We briefly review the results of our paper LBNL-46775: We study certain solutions of left-unilateral matrix equations. These are algebraic equations where the coefficients and the unknown are square matrices of the same order, or, more abstractly, elements of an associative, but possibly noncommutative algebra, and all coefficients are on the left. Recently such equations have appeared in a discussion of generalized Born-Infeld theories. In particular, two equations, their perturbative solutions and the relation between them are studied, applying a unified approach based on the generalized Bezout theorem for matrix polynomials.
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