Hi I need help with a linear algebra problem please.
Let T:R^2->R^2 be the orthogonal projection on the line y=x.
(a) Find a formula for T(x,y)
I don't know where to start on this one because I don't know how to define the transformation.If anyone could explain the transformation and process to find the formula it would be greatly apprerciated.
(b)Use the formula in (a) to show that T^2=T.
Here I just want to know whether T^2 is the composition of T with T?
(c) Find the eigenvalues an bases of the eigenspaces of T.
Here I just need to know how do I set up the matrix whose eigenvalues I must find?
Any input would be greatly appreciated.
Thanks in advance.