1

I would like to rotate a multidimensional vector $v \in R^d$ at a random direction. Now I have two problems here.

  1. How to define direction in a multi dimensional space?
  2. How to rotate the vector in the given direction.

To make it a bit mor cleare I ilusetrate the logic for d=2 and d=3 cases

enter image description here

Now in the d=3 case the blue circle indicates all possible vector which is $\alpha$ away from vector v.

Assume that I am writing a program and I want to call a function such as v = rotateIt(v,direction, alpha). I would expect the function to return the rotated vector. I am having dificulity how to define the direction for any dimension d and also how to rotate the vector towards the given direction with angle alpha. Can anybody give me a solution or direct me to some literature?

Thanks for the help.

DalekSupreme
  • 273

1 Answers1

0
  1. A unit vector can be used to define directions.
  2. Matrix multiplication is a way to rotate a vector.

Two useful links:

Rotation matrix - Wiki

Finding the rotation matrix in n-dimensions

Andy
  • 1