Suppose that I have a 3D matrix, where the $i$-th, $j$-th, $k$-th element is denoted by $h_{ijk}$. The matrix has the dimensions $M\times N \times K$. I want to express the following operation in mathematical notation:
First, compute the standard deviation of the original matrix along the $k$ dimension, which provides an $M\times N$ matrix. Then obtain the average of this matrix along the $i$ dimension, which provides an $N$ element vector. Is the following correct, considering that $\bar{\sigma_{j}}$ represents the $j$-th element of the final resulting vector?
$\bar{\sigma_{j}}=\frac{1}{M}\sum\limits_{i=1}^{M}\sqrt{\frac{\sum\limits_{k=1}^{K}\left(h_{ijk}-\bar{h_{ij}}\right)^2}{K-1}}$ where $\bar{h_{ij}}=\frac{1}{K}\sum\limits_{k=1}^{K}h_{ijk}$
