Surprisingly I found this on MSE: $$\mathrm{tr}(A^T A) = \sum_{i=1}^n \sum_{j=1}^n (a_{ij})^2$$ This result serves my purpose. Rather than take it for granted I would like to be able to actually prove this result and I am not certain how to do it. It seems trivial enough but aside for some special cases of $A$ I just can't see it.
Asked
Active
Viewed 32 times
0
-
Have you tried simply writing down $\operatorname{tr}(A^TA)$ using the definitions of the trace and of the matrix product? – Arnaud D. Apr 20 '17 at 15:40
-
I have. It seems if $A$ is diagonal or symmetric it is easy to show. – Anthony Apr 20 '17 at 15:41
-
It should work perfectly fine for any matrix, even a non-square one. – Arnaud D. Apr 20 '17 at 15:43