# I know it's painful, but could someone check my math?

it also seems to me that this result should have been obtained and published somewhere or documented in a book somewhere, but i dunno where. if someone knows of a reference, i would love to know about it.

TIA.

• right away, i think i am informed of a big error in the swapping of the summation order. – robert bristow-johnson Sep 6 '18 at 21:32
• As the commentor of (math.se) dxiv stated, unless the matrix is symmetric; $A = A^{T}$, the equality wont hold. Cause the left side is summing the lower triangular elements while the right side is summing the upper triangular elements. This assumes that for the element $a_{nk}$, $n$ stands for rows and $k$ stands for $columns$. – Fat32 Sep 6 '18 at 22:57
• yeah, i'm fucking something up. – robert bristow-johnson Sep 6 '18 at 22:59
• @Fat32, i think i groked this upper and lower triangle thing and i fixed the limits in my summations. i hope it's right now, but i would still like someone else to verify. – robert bristow-johnson Sep 7 '18 at 0:10
• I just checked it (on the surface) and it seems ok. – Fat32 Sep 7 '18 at 10:04
• thank you @Fat32 – robert bristow-johnson Sep 9 '18 at 3:04