Orthogonal matrices

• May 9th 2010, 10:00 AM
hmmmm
Orthogonal matrices
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
• May 9th 2010, 05:54 PM
tonio
Quote:

Originally Posted by 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

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

Tonio
• May 9th 2010, 10:00 PM
hmmmm
thanks very much!