User-defined orthonormal basis

[markuz]

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.

 

[CompuChip]

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.

 

[markuz]

thanks

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