There is a technical distinction between a vector and the coordinates of a vector. Are projective (also called "affine") coordinates the coordinates of vectors?(adsbygoogle = window.adsbygoogle || []).push({});

I'm thinking of how translation is accomplished by matrix multiplication. For example the point [itex] (x,y) [/itex] in 2-D is given coordinates [itex] (x,y,1) [/itex] and translation by [itex] (h,v) [/itex] is represented as:

[tex] \begin{pmatrix} 1&0&h \\ 0&1&v \\ 0&0&1 \end{pmatrix} \begin{pmatrix} x \\ y\\ 1 \end{pmatrix} = \begin{pmatrix} x+h \\ y+v \\ 1 \end{pmatrix} [/tex].

Students are told that matrix multiplication performs a linear transformation on a vector space and also disturbed by the exercise showing that translation by a (non-zero) vector is not a linear transformation . What are the saving legalisms here?

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# Projective coordinates vs vectors

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