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Mathematics-Online problems:

Interactive Problem 260: The Differentiation of Polynomials as Linear Map

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A polynomial of degree $ \leq n$ is uniquely defined by the values

$\displaystyle v_p=\big( p(0), \ldots, p(n) \big)^{\operatorname t}.$

Find in each case $ n=1$ and $ n=2$ the matrix $ A$, that maps $ v_p\in \mathbb{R}^{n+1}$ onto the vector $ v_{p'}\in \mathbb{R}^n$ of the derivation $ p'$ of $ p$, i.e. the matrix $ A$ with

$\displaystyle v_{p'}=Av_p \,.$


Solution:


   

(Authors: Höllig/Höfert)

see also:

  automatically generated: 3/12/2018