Miniversal deformations of observable marked matrices. (27th June 2013)

• Record Type: Journal Article
• Authors: Compta, Albert; Ferrer, Josep; Peña, Marta
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 1(2014:Jan. 15)
• Page Start: 20
• Page End: 31
• Publication Date: 2013-06-27
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2780
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2780-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p>Given the set of vertical pairs of matrices <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4t719t0k" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:01704214:media:mma2780:mma2780-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">M</mml:mi><mml:mo class="MathClass-rel">⊂</mml:mo><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo class="MathClass-punc">, </mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo class="MathClass-open">(</mml:mo><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi></mml:mrow><mml:mo class="MathClass-close">)</mml:mo></mml:mrow><mml:mo class="MathClass-bin">×</mml:mo><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo class="MathClass-open">(</mml:mo><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi></mml:mrow><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math></alternatives> keeping the subspace <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4t719szh" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:01704214:media:mma2780:mma2780-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup><mml:mo class="MathClass-bin">×</mml:mo><mml:mrow><mml:mo class="MathClass-open">{</mml:mo><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mo class="MathClass-close">}</mml:mo></mml:mrow><mml:mo class="MathClass-rel">⊂</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math></alternatives> invariant, we compute miniversal deformations of a given pair when it is observable, and the subspace <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4t719sr6" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:01704214:media:mma2780:mma2780-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup><mml:mo class="MathClass-bin">×</mml:mo><mml:mrow><mml:mo class="MathClass-open">{</mml:mo><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mo class="MathClass-close">}</mml:mo></mml:mrow></mml:math></alternatives> is marked. Moreover, we obtain the dimension of the orbit, characterize the structurally stable vertical pairs, and study the effect of each deformation parameter. Copyright © 2013 John Wiley & Sons, Ltd.</p> </abstract>