I fully agree with you on this one. It took us ages to figure out that linear algebra notation it not the right way. Using tensor notation and einsum, tensor and matrix derivatives become almost trivial. And no need to use ugly transposes, Kronecker symbols, etc.. Thats why we wrote this article and created the website. (Sören Laue, creator of this website and my personal biased view)

Thanks for sharing these tools. Do you have any blogs or open access journals sharing this notation? It seems very simple, I'd love to use it