# Show that A is an orthogonal matrix

yoghurt54

## Homework Statement

If {aj} and {bj} are two separate sets of orthonormal basis sets, and are related by

ai = $$\sum$$jnAijbj

Show that A is an orthogonal matrix

Provided above.

## The Attempt at a Solution

Too much latex needed to show what I tried, but basically I considered the properties of an orthogonal matrix: AAT = 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 that aj.ak = o if j and k are different and 1 if they are the same, and the same for the vectors bj.

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