Linear Map Conditions for Defining a Map on Projective Spaces

[latentcorpse]

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

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

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

not a scooby.

 

[Dick]

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?