1. ## Orthogonal Matrix

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

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

2. Originally Posted by dwsmith
Prove that the transpose of an orthogonal matrix is an orthogonal matrix.

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

What's the definition of "orthogonal matrix" you have? One of the equivalent ones is that a (real) square matrix $A$ is orthogonal iff $A^{-1}=A^t\Longleftrightarrow AA^t=I$ .

From here that your problem has an almost trivial proof.

Tonio

3. $(AA^{T})^{T}=(A^{T})^{T}A^{T}=AA^{T}=I$

Therefore, the transpose of an orthogonal matrix is orthogonal.

4. Originally Posted by dwsmith
$(AA^{T})^{T}=(A^{T})^{T}A^{T}=AA^{T}=I$

Therefore, the transpose of an orthogonal matrix is orthogonal.

Indeed

Tonio