If A and B are both orthogonal nxn matrices.

Can anyone show That AB is orthogonal...

Thanks

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- Apr 21st 2006, 06:40 AMdopiOrthogonal
If A and B are both orthogonal nxn matrices.

Can anyone show That AB is orthogonal...

Thanks - Apr 21st 2006, 11:57 AMdopiOrthogonal problem
If A and B are both orthogonal nxn matrices.

Can anyone show That AB is orthogonal...iv been stuck on this question for a while now

Thanks - Apr 21st 2006, 12:19 PMCaptainBlackQuote:

Originally Posted by**dopi**

$\displaystyle AA^T=I$

Now suppose $\displaystyle A$ and $\displaystyle B$ be orthogonal, and let

$\displaystyle C=AB$. Now $\displaystyle C^T=B^TA^T$, so:

$\displaystyle

CC^T=ABB^TA^T=AIA^T=AA^T=I

$

Hence $\displaystyle C$ is orthogonal.

RonL - Apr 21st 2006, 01:40 PMdopiQuote:

Originally Posted by**CaptainBlack**

Say if you add A and B (A+B)...would that be Orthognal? - Apr 21st 2006, 10:07 PMCaptainBlackQuote:

Originally Posted by**dopi**

RonL - Apr 22nd 2006, 02:26 AMTD!
From the definition, we have for A and B:

$\displaystyle

\begin{array}{l}

AA^{ - 1} = A^{ - 1} A = I \\

BB^{ - 1} = B^{ - 1} B = I \\

\end{array}

$

$\displaystyle

\left( {AB} \right)\left( {AB} \right)^{ - 1} = ABB^{ - 1} A^{ - 1} = AIA^{ - 1} = AA^{ - 1} = I

$ - Apr 22nd 2006, 03:19 AMCaptainBlackDon't make duplicate posts
Don't post the same question in two different fora.

I have merged these two because they both have responses.

RonL - Apr 22nd 2006, 03:26 AMCaptainBlackQuote:

Originally Posted by**TD!**

RonL