(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If {a_{j}} and {b_{j}} are two separate sets of orthonormal basis sets, and are related by

a_{i}= [tex]\sum[/tex]_{j}^{n}A_{ij}b_{j}

Show that A is an orthogonal matrix

2. Relevant equations

Provided above.

3. The attempt at a solution

Too much latex needed to show what I tried, but basically I considered the properties of an orthogonal matrix: AA^{T}= I and considered which elements would multiply and sum to give the 1's and 0's of the identity matrix.

I then considered the fact thata_{j}.a_{k}= o if j and k are different and 1 if they are the same, and the same for the vectorsb_{j}.

Then I thought of the property of preserving norms, but can't see how to connect it to this problem.

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# Homework Help: Show that A is an orthogonal matrix

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