Determinant of the Wronskian
The Wronksian of functions
is the matrix determinant
. Its derivative is the matrix determinant
(that is, the previous matrix with a different bottom row). It’s an interesting exercise to prove this, so let’s do that.
We take the derivative, applying our induction assumption, obtaining
But the bracketed part is just
Nick
Nice proof! Does this mean you’re going to specialize in analysis and differential equations next year? Or is it the (linear) algebra in this proof that appeals to you most?
22 Jul 2012, 11:13
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