- #1

yoghurt54

- 19

- 0

## Homework Statement

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

## Homework Equations

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: 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 that

**a**

_{j}.

**a**

_{k}= o if j and k are different and 1 if they are the same, and the same for the vectors

**b**

_{j}.

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