Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
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)
[Links]
  automatisch erstellt am 12.  3. 2018