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Is there a special or distinct term for a projection that is essentially just a 'truncation', i.e. a projection that simply eliminates some number of dimensions?

For example the projection $P=[I_2 \; \; 0 ]$ (for $I_2$ the 2 dimensional identity matrix). If we have some set of variables $\mathbf{x}=(x_1,x_2,x_3)^T$, then $\tilde{\mathbf{x}}=P\mathbf{x}$ is simply a 'truncated' set of variables where $x_3$ has been eliminated.

Dovetailed
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    Every projection is of this type if you pick the correct basis, so no, there is no special name for this. – 5xum Feb 25 '14 at 12:59
  • Sorry, yes, that was stupidly put of me. I was asking because I wanted to talk about every projection being decomposed into a transformation and a 'truncation' step, as it makes it easier to compare several methods in something I'm writing. – Dovetailed Feb 25 '14 at 13:14

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I'd call them projections along an axis/axes, because the direction is parallel to an axis/axes.

Mark S.
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