Abstract
Checking linear dependence of a finite number of vectors is a basic problem in linear algebra. We aim to extend the theory of linear dependence to parametric vectors where the entries are polynomials. This dependency depends on the specifications of the parameters or values of the variables in the polynomials. We propose a new method to check if parametric vectors are linearly dependent. Furthermore, this new method can also give the maximal linearly independent subset, and by which the remaining vectors are expressed in a linear combination. The new method is based on the computation of comprehensive Gröbner system for a finite set of parametric polynomials.
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Acknowledgements
This work was supported in part by the Chinese Universities Scientific Fund (Grant No. 2017QC061), and the National Natural Science Foundation of China (Grant No. 11371356).
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Ma, X., Sun, Y., Wang, D., Xue, Y. (2017). On Checking Linear Dependence of Parametric Vectors. In: Huang, DS., Jo, KH., Figueroa-GarcÃa, J. (eds) Intelligent Computing Theories and Application. ICIC 2017. Lecture Notes in Computer Science(), vol 10362. Springer, Cham. https://doi.org/10.1007/978-3-319-63312-1_17
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DOI: https://doi.org/10.1007/978-3-319-63312-1_17
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