Linear Projection

Linear Algebra
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Riemann
Posts: 176
Joined: Sat Nov 14, 2015 6:32 am
Location: Melbourne, Australia

Linear Projection

#1

Post by Riemann »

Let $\mathcal{V}$ be a linear space over $\mathbb{R}$ such that $\dim_{\mathbb{R}} \mathcal{V} < \infty$ and $f:\mathcal{V} \rightarrow \mathcal{V}$ be a linear projection such that any non zero vector of $\mathcal{V}$ is an eigenvector of $f$. Prove that there exists $\lambda \in \mathbb{R}$ such that $f = \lambda \; \mathrm{Id}$ where $\mathrm{Id}$ is the identity endomorphism.
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
S.F.Papadopoulos
Posts: 16
Joined: Fri Aug 12, 2016 4:33 pm

Re: Linear Projection

#2

Post by S.F.Papadopoulos »

$f=I$
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Riemann
Posts: 176
Joined: Sat Nov 14, 2015 6:32 am
Location: Melbourne, Australia

Re: Linear Projection

#3

Post by Riemann »

Hi ,

I'm sorry but I do not understand what exactly you wrote down! Could you please elaborate?
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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