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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)

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  automatisch erstellt am 12.  3. 2018