Recent content by Doradus

Homework Statement Be V the set ##\{f \in \mathbb{R}[X]| deg\,f \leq 2 \}##. This becomes to an euclidic vector space through the inner product ##\langle f,g\rangle:=\sum_{i=-1}^1f(i)g(i)## . The same goes for ##\mathbb{R}## with the inner product ##\langle r,s\rangle :=rs\,\,\,##. a) For...

Hello, i need a little help. Did someone have an idea how to prove this? Thanks in advance. Be ##\Phi## an direct isometry of the euclidean Space ##\mathbb{R}^3## with ##\Phi (\begin{pmatrix} 2\\0 \\1 \end{pmatrix})##=##\begin{pmatrix} 2\\1 \\0 \end{pmatrix}## and ##\Phi (\begin{pmatrix}...

##\Phi |_W## is the same as ##\Phi(W)## ##id_W## is the identity funktion ##\Phi(w)=w## ##D_{BB}## Matrix with basis B ##D_{SS}## Matrix with basis S ##D_{BS}## I am not sure. :-) Well, because I'm not sure, what ##D_{BS}## means, i think c) is not that important. I'm more interested in a) and b).

Hello, i'm trying to prove this statements, but I'm stuck. Be ##V=R^n## furnished with the standard inner product and the standard basis S. And let W ##\subseteq## V be a subspace of V and let ##W^\bot## be the orthogonal complement. a) Show that there is exactly one linear map ##\Phi:V...