# Gram-Schmidt Orthonormalization

In the paper from Kulkarni et al., 2011 (Appendix B1), a method is given for transforming from Boyer-Lindquist (BL) coordinates to a comoving frame.

This involves using Gram-Schmidt orthonormalization to determine the components of the transformation matrix $\Lambda$, that transforms the BL coordinates $e_{\nu}$ to the comoving frame coordinates $e_{\hat{\nu}}$. i.e.

$$e_{\hat{\nu}} = \Lambda e_{\nu}$$

Can anyone give an explicit example as to how this is done?

I understand the Gram-Schmidt process as described in the linked Wikipedia article, but cannot see how to use this process to determine the components of the transformation matrix.

Any help greatly appreciated.

• This seems to be a linear algebra question rather than a physics question - you seem to be asking how to obtain the transformation matrix between two given bases of a vector space. What's the physics content here? – ACuriousMind Apr 11 '17 at 15:46
• Sorry maybe I should have been more explicit; the physics content comes from the context transforming between reference frames within a (e.g.) Kerr spacetime. If not appropriate I can move the question. – user1887919 Apr 11 '17 at 15:58