Minimal polynomial systems for parametric matrices |
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| Authors: | Amir Hashemi Benyamin M-Alizadeh Mahdi Dehghani Darmian |
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| Institution: | 1. Department of Mathematical Sciences , Isfahan University of Technology , Isfahan 84156-83111 , Iran Amir.Hashemi@cc.iut.ac.ir;3. Young Researchers Club, Science and Research Branch , Islamic Azad University , Tehran , Iran;4. Department of Mathematics, Science and Research Branch , Islamic Azad University , Tehran , Iran |
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| Abstract: | In this article, we study the minimal polynomials of parametric matrices. Using the concept of (comprehensive) Gröbner systems for parametric ideals, we introduce the notion of a minimal polynomial system for a parametric matrix, i.e. we decompose the space of parameters into a finite set of cells and for each cell we give the corresponding minimal polynomial of the matrix. We also present an algorithm for computing a minimal polynomial system for a given parametric matrix. |
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| Keywords: | minimal polynomial Gröbner bases Gröbner systems |
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