Simplifying matrix differential equations with general coefficients
- Resource Type
- Original Paper
- Authors
- Tsui, Man Cheung
- Source
- Israel Journal of Mathematics. :1-19
- Subject
- Language
- English
- ISSN
- 0021-2172
1565-8511
We show that the n × n matrix differential equation δ(Y) = AY with n2 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.