# orthogonal matrices help

• Mar 9th 2011, 01:39 PM
eleahy
orthogonal matrices help
using the definition of an orthogonal matrix prove :
P is an orthogonal matrix if and only if P^t is an orthogonal matrix.

I know P is orthogonal if we can multiply P by P^t and get the identity matrix but dont know where to go from there!!
any help appreciated!!
• Mar 9th 2011, 01:46 PM
Drexel28
Quote:

Originally Posted by eleahy
using the definition of an orthogonal matrix prove :
P is an orthogonal matrix if and only if P^t is an orthogonal matrix.

I know P is orthogonal if we can multiply P by P^t and get the identity matrix but dont know where to go from there!!
any help appreciated!!

Just use the fact that $\left(P^{\top}\right)^{-1}=\left(P^{-1}\right)^{-1}=P$ and so $\left(P^{\top}\right)^{-1}=P=\left(P^{\top}\right)^{\top}$.
• Mar 9th 2011, 02:16 PM
eleahy
still not exactly sure but have stuff to work with ill figure it thanks so much :)