I need to create a matrix given some information, without the matrix it is impossible to continue the assignment - unfortunately, I don't find much relevant information on canonical basis online, well, I have found a few examples, but they are similar to what I'm looking at...
Find the 2x2-matrix, A, belonging to the linear "map"/"projection", T, with regard to the canonical basis of R^2 (real numbers).
A small note e(1) means e sub one.
T(e(1) + e(2)) = e(1) + e(2), T(-e(1)+e(2)) = (1/2)e(1) - (1/2)e(2)
Does anyone have an idea on this matter?
Thanks in advance.