论文标题
简化具有一般系数的矩阵微分方程
Simplifying matrix differential equations with general coefficients
论文作者
论文摘要
我们表明，$ n \ times n $矩阵微分方程$δ（y）= ay $，$ n^2 $一般系数无法通过使用量子系数在$ a $ a $ a $ a及其衍生物的矩阵条目中的理性函数来简化为少于$ n $参数的方程。我们的证明使用差异性galois理论和基本维度的差异类似物。我们还限制了描述一些通用Picard-vessiot扩展所需的最小参数数量。
We show that the $n\times n$ matrix differential equation $δ(Y)=AY$ with $n^2$ general coefficients cannot be simplified to an equation in less than $n$ parameters by using gauge transformations whose coefficients are rational functions in the matrix entries of $A$ and their derivatives. Our proof uses differential Galois theory and a differential analogue of essential dimension. We also bound the minimum number of parameters needed to describe some generic Picard-Vessiot extensions.
