Simplifying matrix differential equations with general coefficients
| Autor: | Tsui, Man Cheung |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We show that the $n\times n$ matrix differential equation $\delta(Y)=AY$ 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. Comment: 13 pages. Corrected miscitation of [1] on page 5; added Example 2.2; small grammatical change |
| Databáze: | arXiv |
| Externí odkaz: |
|