Let $ \operatorname{Gal} ( \mathcal{L} ) = \operatorname{Gal}_\partial ( L/K ) = \operatorname{Aut}_{(K , \partial )} ( L , \partial ) $ be the algebraic subgroup of the group $ \operatorname{Aut} ( \operatorname{Sol} ( \mathcal{L} , * ) ) \simeq GL_m ( \mathbb{C} ) $ of invertible linear transformations of the solution space $ \operatorname{Sol} ( \mathcal{L} , * ) $ of the linear differential equation $ \mathcal{L} $ of order $ m $ at some point $ * $ which form a $m$-dimentional vector space over $\mathbb{C} $.
$ ( L , \partial ) $ is the differential field obtained by adjoining all solutions of $ \mathcal{L} $ and their derivative over $ (K, \partial ) $, the differential field of rationally known quantities.
My question is : Why is : $ \operatorname{tr} \deg_K L = \dim \operatorname{Gal} ( \mathcal{L} ) $ ?
Thanks in advance for your help.