# matrix orthogonal

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• May 9th 2008, 02:53 AM
deragon999
matrix orthogonal
This is probably easier than I think it looks but..im stumped...
Here goes

A is an n x n orthoganal matrix...show that a^t(transpose of a) is also orthoganal

Thanks in advance
• May 9th 2008, 03:30 AM
mr fantastic
Quote:

Originally Posted by deragon999
This is probably easier than I think it looks but..im stumped...
Here goes

A is an n x n orthoganal matrix...show that a^t(transpose of a) is also orthoganal

Thanks in advance

It follows from the definition! Read

Orthogonal matrix - Wikipedia, the free encyclopedia

to see what I mean ....
• May 9th 2008, 10:23 AM
Moo
Hello,

Quote:

Originally Posted by deragon999
This is probably easier than I think it looks but..im stumped...
Here goes

A is an n x n orthoganal matrix...show that a^t(transpose of a) is also orthoganal

Thanks in advance

A matrix A is orthogonal if $A^{-1}=A^t$

By taking the transpose in each side, we have :

$(A^{-1})^t=(A^t)^t$

$\implies (A^t)^{-1}=(A^t)^t$

Hence $A^t$ is orthogonal...