Abstract
In this paper we define the Popov and weak Popov forms of matrices over Poincaré–Birkhoff–Witt (PBW) extensions, and exhibit effective algorithms to find them. As applications we give general methods to calculate the ranks of such matrices, and a method to transfer a system of differential equations into a first order equation.
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Acknowledgments
All the authors would like to thank NSERC Canada for their support of this research.
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Giesbrecht, M., Labahn, G., Zhang, Y. (2014). Computing Popov Forms of Matrices Over PBW Extensions. In: Feng, R., Lee, Ws., Sato, Y. (eds) Computer Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43799-5_6
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DOI: https://doi.org/10.1007/978-3-662-43799-5_6
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