why absolute square of matrix equal matrix by transpose

Question

I want to understand why is $ |e^2| = e^T * e $ I find this formula a lot while studying deep learning like in here

Answer 1

It isn't $\lvert e^2\rvert$, but $\lvert e\rvert^2$, and it is more about column vectors ($(n\times 1)$ matrices) than it is about matrices. The identity holds provided that $\lvert x\rvert$ stands for the usual Euclidean norm $\sqrt{\sum_{j=1}^n x_j^2}$ on $\Bbb R^n$. And, well, it's just the fact that for column vectors $y^Tx=\sum_{j=1}^n y_ix_i$.