Prove Orthogonal Matrix Transpose is Orthogonal

[Dustinsfl]

Prove that the transpose of an orthogonal matrix is an orthogonal matrix.

I think that the Kronecker delta needs to be used but not sure how to write it out.

 

[Fredrik]

Do you know the definition of an orthogonal matrix?

 

[Dustinsfl]

The columns most for an orthogonal set.

 

[Mark44]

The columns most for an orthogonal set.

Wouldn't that be information you should include in your first post, as either given/known data or relevant equations?

That's why those sections are in the problem template. We shouldn't have to pry that information out of you.

 

[Dustinsfl]

Wouldn't that be information you should include in your first post, as either given/known data or relevant equations?

I find that trivial because if I didn't know that, why would I be trying to prove anything related to orthogonal matrices?

 

[Mark44]

How do we know that you know that? Our only evidence of what you know or don't know is the information you include.

 

[Dustinsfl]

Because I have no business trying to prove something I know nothing about.

 

[Mark44]

So convince us that you know something about it by including the basic information when you post.

 

[Fredrik]

There's another definition of "orthogonal matrix" that's more common (I think), and definitely more useful in this case. (It makes the problem trivial). Do you know any other statements about orthogonal matrices? Something that holds if, and only if, the columns are mutually orthogonal?