If A is an orthogonal matrix, then there must exist a symmetric invertible matrix S such that S1AS is diagonal.
7/26/2017 OneNote Online 2.6 Monday, September 8, 28:51 PM https://onedrive.live.com/view.aspxref=button&Bsrc=SMIT&resid=36773184373A8F0B!2562&cid=36773184373a8f0b&app=OneNote&authkey=Avz_e_hLmB4xJLw 1/5 7/26/2017 OneNote Online https://onedrive.live.com/view.aspxref=button&Bsrc=SMIT&resid=36773184373A8F0B!2562&cid=36773184373a8f0b&app=OneNote&authkey=Avz_e_hLmB4xJLw 2/5