Throughout this presentation I have chosen to use a symbolic matrix notation. This choice was not made lightly. I am a strong advocate of index notation, when appropriate. For example, index notation greatly simplifies the presentation and manipulation of differential geometry. As a rule-of-thumb, if your work is going to primarily involve differentiation with respect to the spatial coordinates, then index notation is almost surely the appropriate choice. In the present case, however, I will be manipulating large systems of equations in which the matrix calculus is relatively simply while the matrix algebra and matrix arithmetic is messy and more involved. Thus, I have chosen to use symbolic notation.
CITATION STYLE
Zhang, X.-D. (2020). Matrix Differential. In A Matrix Algebra Approach to Artificial Intelligence (pp. 55–87). Springer Singapore. https://doi.org/10.1007/978-981-15-2770-8_2
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