# Orthogonal matrices

#### hmmmm

ok i've done this proof before, its pretty simple but i cant seem to do it now, and i have an exam tomorrow......
how do you show that Av.Au=v.u where A is an orthogonal matrix and u and v are vectors,
thanks for any help

#### tonio

ok i've done this proof before, its pretty simple but i cant seem to do it now, and i have an exam tomorrow......
how do you show that Av.Au=v.u where A is an orthogonal matrix and u and v are vectors,
thanks for any help

It is practically the definition of orthogonal matrix! Since $$\displaystyle A^{-1}=A^{*}$$ , $$\displaystyle Av\cdot Au=v\cdot A^{*}Au=v\cdot Iu=v\cdot u$$

Tonio

hmmmm

#### hmmmm

thanks very much!