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Describe the space that $A$ projects onto and the space that $A$ projects along$$A = \begin{bmatrix} 0 & 1 \\0&1 \end{bmatrix}.$$

A matrix, $M$ is a perpendicular projection operator on the column space of $M \iff MM = M $ and $M = M^T.$ Clearly, $A$ does not satisfy this theorem. How do I describe the space that $A$ projects onto and the space that $A$ projects along? I need help.

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First you need to check that $A$ projects, that is $A^2=A$. That is true.

Then the subspace it projects to is the range of $A$ (I hope you can find it) and the space it projects along is the nullspace of $A$ (you should be able to find it too).

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  • $\begingroup$ I appreciate your help $\endgroup$ – holala Aug 30 at 19:59
  • $\begingroup$ You can probably accept the answer. $\endgroup$ – JCAA Aug 30 at 20:09
  • $\begingroup$ Can yo take a look at this question I posted here math.stackexchange.com/questions/3804609/…. I will appreciate your help there too $\endgroup$ – holala Aug 30 at 20:13
  • $\begingroup$ The second answer there is correct. The first one is totally wrong provided $n\ge 2$ and rank$(A)<n$ $\endgroup$ – JCAA Aug 30 at 20:20
  • $\begingroup$ You mean the answer provided by Draditate is correct? $\endgroup$ – holala Aug 30 at 20:23

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