Topology calculation help

  • #1
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Let [itex]\mathbb{RP}^n= ( \mathbb{R}^{n+1} - \{ 0 \} ) / \sim[/itex] where [itex]x \sim y[/itex] if [itex]y=\lambda x, \lambda \neq 0 \in \mathbb{R}[/itex] adn the equivalence class of [itex]x[/itex] is denoted [itex][x][/itex].

what is the necessary and sufficient condition on the linear map [itex]f : \mathbb{R}^{n+1} \rightarrow \mathbb{R}^{m+1}[/itex] for the formula [itex][f][x]=[f(x)][/itex] to define a map

[itex][f] : \mathbb{RP}^n \rightarrow \mathbb{RP}^m ; [x] \mapsto [f(x)][/itex]

not a scooby.
 
  • #2


Well, it has to respect your equivalence relation, right? Map lines through the origin into lines through the origin. How can a linear f not do that?
 

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