# Rotation matrix multiplied by matrix of column vectors?

Hey, let's say that in 2D space we have a 2x2 rotation matrix R. Normally you could multiply this rotation matrix by a 2x1 column matrix / vector X. In that case it would be XR to get the vector rotated in the way described by R. Now what I'm wondering is, what if I had 3 column vectors that I wanted to combine and multiply column-wise. Is there a mathematical way to describe having this new matrix and doing the operation on each column individually, then putting it back into the same type of matrix? As in I want to multiply X0, X1, X2, individually by R but describe it in a simple way. I don't think I can say XR in this case... can I?

mathwonk
Homework Helper
in my notation i think you meant RX for X rotated by R. Then RZ, where Z is a matrix of any number of columns, is a matrix whose columns are the result of rotating all those columns by R.

Sorry, you are right I meant RX. Are you saying that if I have multiple vectors in one matrix, where each column is a vector, I can just multiply the rotation matrix by that matrix to rotate each individual vector? Or is there another way I'd need to do this?

mathwonk
Homework Helper
i don't understand. are you asking me to repeat my statement? couldn't you just read it again?

Well it doesn't really make sense to me, because you are basically saying I can multiply a 2x2 matrix by a 2xn matrix which I don't think is possible for n>2? In my case I have a 2x3 matrix, i.e. 3 column vectors and a 2x2 rotation matrix

mathwonk