# A Linear Transformation question

• November 7th 2010, 07:33 AM
jayshizwiz
A Linear Transformation question
give an example of a linear transformation $\, T:R^2 \rightarrow R^2$ where $T^2=T$ and $0,1$ are the eigenvalues.

Attempt:
$
T(x,y) = (x,0)$

$*T(T(x,y) = T(x,0) = (x,0)$
$*T(x,y) = (x,0)$

$T(1,0) = (1,0) = 1(1,0)$
$T(0,1) = (0,0) = 0(0,1)$

Is this correct?

Thanks!
• November 7th 2010, 12:25 PM
HallsofIvy
Yes, that's exactly right! Any linear transformation that satifies " $T= T^2$" is a "projection" onto some subspace. Here, you chose to project onto the x-axis.

Any one dimensional subspace of $R^2$ is a line through the origin, (x, y)= (x, ax) for some number a (or the y-axis, (0, y)). It's not easy but you might try to find the projection that maps $(x_0, y_0)$ onto that line.