Transpose of orthogonal matrix

td21
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Homework Statement



Orthogonal matrix means Q^{T}Q=I, but not necessary QQ^{T}=I, so why can we say the inverse of Q is Q^{T}?

Homework Equations





The Attempt at a Solution


the attempt is actually in my question. It's something i don't understand when doing revision.
 
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addition:
is <br /> QQ^{T}=I<br />
100% true?If it is, my problem is solved.
 
td21 said:
addition:
is <br /> QQ^{T}=I<br />
100% true?If it is, my problem is solved.

Sure. Q^TQ=I implies QQ^T=I.
 
An interesting variation is when Q has more rows than columns. In this case, QTQ still equals I but QQT doesn't.
 

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