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Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood.
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A mixed Vandermonde-Wronskian matrix
I am trying to prove that a matrix of the following form is generically nonsingular:
$A= \begin{bmatrix}
1&1&1&1 \\
f_1 & f_2 & f_3 &f_4 \\
(f_1 -\frac{d}{dt}).f_1& (f_2 -\frac{d}{dt}).f_2 & (f_ …