Mathematik-Online problems: Problem 535: Linear Maps in the Vector Space of Polynomials

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	Mathematik-Online problems:
	Problem 535: Linear Maps in the Vector Space of Polynomials

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

The following linear maps $p\longmapsto q$ map polynomials of degree $\le m$ onto polynomials of degree $\le n$ . Find the matrix representation with respect to the monomial basis.

a): $m=n=2,\quad q(x) = p(x+1)$
b): $m=n-2=2,\quad q(x) = (x^2+1) p(x)$
c): $m=n/2=2,\quad q(x) = p(x^2+1)$

(Authors: Höllig / Höfert)

see also:

Keyword: Vector space
Keyword: Polynomial
Keyword: Matrix
Keyword: Map: linear

automatisch erstellt am 12. 3. 2018