Mathematik-Online problems: Problem 115: Differentation as Linear Map

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	Mathematik-Online problems:
	Problem 115: Differentation 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)

Let

, defined by

, be the map on the set of all real functions that are differentiable for all degrees of differentiation.

i): Show that is linear.
ii): Give all eigenvalues of .
iii): Find an eigenfunction of , corresponding to the eigenvalue $\lambda$ , i.e. a function $f\neq 0$ with $Df=\lambda f$ .

b)

Let $P_4(\mathbb{R})$ be the vector space of the real polynomials of degree $\leq 4$ , and let

, defined by

, be the map of $P_4(\mathbb{R})$ onto itself. Find the matrix representation of

with respect to the basis $B=\{1, x, x^2, x^3, x^4\}$ .

(Authors: Apprich/Höfert)

Solution:

automatisch erstellt am 14. 10. 2004