Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rotation matrix multiplied by matrix of column vectors?

  1. Jan 20, 2015 #1
    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?

    5sanU8q.png
    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?
     
  2. jcsd
  3. Jan 20, 2015 #2

    mathwonk

    User Avatar
    Science Advisor
    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.
     
  4. Jan 20, 2015 #3
    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?
     
  5. Jan 20, 2015 #4

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    i don't understand. are you asking me to repeat my statement? couldn't you just read it again?
     
  6. Jan 20, 2015 #5
    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
     
  7. Jan 21, 2015 #6

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    ok, in matrix multiplication AB you dot the rows of the left matrix A by the columns of the right matrix B. so a 2x2 matrix A can be multiplied by any matrix B with 2 rows, i.e. any 2xn matrix. do you agree?

    in general, matrix multiplication is defined for any mxn matrix times any nxk matrix. i think i got this right. what do you think?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook