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A theorem of the alternatives for the equation |Ax| − |B||x| = b

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Abstract

A theorem of the alternatives for the equation \({|Ax|-|B||x|=b\ (A,B\in{\mathbb{R}}^{n\times n},\, b\in{\mathbb{R}}^n)}\) is proved and several consequences are drawn. In particular, a class of matrices A, B is identified for which the equation has exactly 2n solutions for each positive right-hand side b.

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Authors and Affiliations

  1. Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic

    Jiri Rohn

  2. School of Business Administration, Anglo-American University, Prague, Czech Republic

    Jiri Rohn

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  1. Jiri Rohn
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Correspondence to Jiri Rohn.

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Supported by the Czech Republic Grant Agency under grants 201/09/1957 and 201/08/J020, and by the Institutional Research Plan AV0Z10300504.

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Rohn, J. A theorem of the alternatives for the equation |Ax| − |B||x| = b . Optim Lett 6, 585–591 (2012). https://doi.org/10.1007/s11590-011-0284-4

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  • DOI: https://doi.org/10.1007/s11590-011-0284-4

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