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User-defined orthonormal basis

  1. Apr 23, 2013 #1
    Does anybody know how to create a orthonormal basis, i.e. a matrix containing orthogonal vectors of norm 1, out of a given direction (normalised vector or versor) in a space with dimension N>3?
    With "out of a given direction", I mean that the resulting basis would have the first vector equal to the provided versor.
  2. jcsd
  3. Apr 23, 2013 #2


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    In principle, all you need is to find N - 1 more linearly independent vectors, and then you can apply the Gram-Schmidt process. That preserves the first vector, so if you put your given vector first in the list it will remain unaltered.
  4. Apr 23, 2013 #3

    Thanks it works! Not sure about the numerical stability but will keep an eye on it.
    Thanks again
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