Orthogonal matrices

Dec 2008
288
13
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
 
Oct 2009
4,261
1,836
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
 
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