Transpose of orthogonal matrix

td21 · Feb 28, 2011

Homework Statement

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

the attempt is actually in my question. It's something i don't understand when doing revision.

td21 · Feb 28, 2011

addition:
is [itex] QQ^{T}=I[/itex]
100% true?If it is, my problem is solved.

Dick · Feb 28, 2011

td21 said:

addition:
is [itex] QQ^{T}=I[/itex]
100% true?If it is, my problem is solved.

Sure. Q^TQ=I implies QQ^T=I.

hotvette · Feb 28, 2011

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