High Quality Content by WIKIPEDIA articles! In mathematics, the Pincherle derivative of a linear operator scriptstyle{ T:mathbb K[x] longrightarrow mathbb K[x] } on the vector space of polynomials in the variable scriptstyle x over a field scriptstyle{ mathbb K} is another linear operator scriptstyle{ T':mathbb K[x] longrightarrow mathbb K[x] } defined as T' = [T,x] = Tx-xT = -operatorname{ad}(x)T,, so that T'{p(x)}=T{xp(x)}-xT{p(x)}qquadforall p(x)in mathbb{K}[x]. In other words, Pincherle derivation is the commutator of scriptstyle{T} with the multiplication by scriptstyle x in the algebra of endomorphisms scriptstyle{ operatorname{End} left( mathbb K[x] right) }.

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