The matrix is | 1/2 -1/2 | | 1/2 1/2 | Why is this matrix not representing a rotation? The form of rotation is | cos x -sin x | |sin x cos x | So in this case tan x = 1 and so x = 45...isn't this rotation of 45 degrees? On similar note, for the matrix | 5 6 | | -6 5 | it says it is a rotation of [itex]\theta[/itex] = arctan (-6/5), which I assumed was obtained by saying that cos x = 5 and sin x = -6 so tan x = -6/5....so what is the difference between this example and my problem? edit: for the second example, it actually states that this matrix is a rotation combined with scaling. Is this the main reason why the first problem can't be considered just rotation? Because it is actually also scaled? I mean that the rotation formula I gave was derived using the unit vectors, but the vectors represented by the first problem are not unit because their length is 1/2 not 1....? Idk this seems like trivial difference though..