# Thread: matrix orthogonal

1. ## 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

2. 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 ....

3. Hello,

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 $\displaystyle A^{-1}=A^t$

By taking the transpose in each side, we have :

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

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

Hence $\displaystyle A^t$ is orthogonal...