ABSTRACT
Note that two different identity matrices are involved in this equation: AtA is an n×n matrix, while AAt is m×m. Be careful not to confuse them. We can prove this identity by induction also. First, for k=1, the result is obvious. Assume that it is true for every n=k; then, for n=k+1,
which proves the desired result. Here, I have used equation (39) to get from the third line to the fourth line above.
