What is the name of this color transformation?
I do not know the name of your transformation $T$, but it can't be the Karhunen-Loeve transform: The Karhunen-Loeve transform is image specific and its transformation matrix is a rotation matrix (see for example the KLT in Mathematica).

Given the values in your matrix, it seems to attempt to separate between intensity (first row) and color (the other two rows, spanning the remaining hyperplane) while being  optimized for speed.