How should I denote vectors and matrices in equations when accessing contents within in a scientific paper?

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I come mainly from a software background and my math is not as strong as my programming. I am writing a paper and cover the basics of neural networks. As an example, here is what I have in terms of some equations:

$$ n_j^{(\ell)} = \sum_{i=1}^{N_{\ell-1}} a_i^{(\ell-1)} w_{ij}^{(\ell)} + b_j^{(\ell)}, \quad j=1, 2, \ldots, N_\ell. $$

Here, $w_{ij}$ accesses a matrix which I introduce alone as $W$ earlier. My question is should I change the format depending on what is returned? For example, $\mathbf{b}$ is a vector and I access a scalar at $b_j$, so I print it in italics as opposed to bold. Is this correct? I apologise the question is somewhat open, I am new to this!