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In mathematics, the Pincherle derivative[1] of a linear operator on the vector space of polynomials in the variable x over a field is the commutator of with the multiplication by x in the algebra of endomorphisms . That is, is another linear operator
(for the origin of the notation, see the article on the adjoint representation) so that
This concept is named after the Italian mathematician Salvatore Pincherle (1853–1936).
^Rota, Gian-Carlo; Mullin, Ronald (1970). Graph Theory and Its Applications. Academic Press. pp. 192. ISBN 0123268508.
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In mathematics, the Pincherlederivative T ′ {\displaystyle T'} of a linear operator T : K [ x ] → K [ x ] {\displaystyle T:\mathbb {K} [x]\to \mathbb...
Third International Congress of Mathematicians. The Pincherlederivative is named after him. Pincherle was born into a Jewish family in Trieste (then part...
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degree, he worked in Bologna as an assistant to the chair of Salvatore Pincherle until 1900. From 1900 to 1906, he was a senior high school teacher, first...
dimension, but Peano did not develop that theory further. In 1897, Salvatore Pincherle adopted Peano's axioms and made initial inroads into the theory of infinite-dimensional...
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Global Information
![{\displaystyle T:\mathbb {K} [x]\to \mathbb {K} [x]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3258999b37e031c221d4fe0907c0aefb540ebc1a)
![{\displaystyle \operatorname {End} (\mathbb {K} [x])}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e54c48522eacff130c49470eb25962a1274efcee)
![{\displaystyle T':\mathbb {K} [x]\to \mathbb {K} [x]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1004d559f5f528d5450e605804e987f11fbf37e7)
![{\displaystyle T':=[T,x]=Tx-xT=-\operatorname {ad} (x)T,\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/adeaa560041ded4e7cc9ef6d1ee77550949a01d8)
![{\displaystyle T'\{p(x)\}=T\{xp(x)\}-xT\{p(x)\}\qquad \forall p(x)\in \mathbb {K} [x].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/25baff00a3c5ca6de0647d4daf76c6622b41b421)