How do you show that a linear transformation is idempotent?
T:R^3 to R^3 T (x y z)^T = (0.5 (x-z) , y, 0.5 (z-x))
I have no idea where to begin. I know a few facts about idempotent properties e.g such as their eigenvalues are either 0 or 1. How would I show that the above transformation has these eigenvalues. I know how to find them but the above form has thrown me off. Would I have to just prove a couple of idempotent to show it is idempotent?
Thanks in advance
T:R^3 to R^3 T (x y z)^T = (0.5 (x-z) , y, 0.5 (z-x))
I have no idea where to begin. I know a few facts about idempotent properties e.g such as their eigenvalues are either 0 or 1. How would I show that the above transformation has these eigenvalues. I know how to find them but the above form has thrown me off. Would I have to just prove a couple of idempotent to show it is idempotent?
Thanks in advance
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