My school offers Matrix Calculus class next semester. I have never heard about this subject before and got intrigued. After a short chat with professor I found myself unable to get rid of suspicion that matrix calculus might just be simplified version or a special case of Tensor Calculus/Tensor Analysis. Moreover, the first sentence in Wikipedia article about Matrix Calculus says
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus
I have been self-studying tensor analysis for a little and took multiple classes related multivariable calculus. Does it worth to take this class for someone focusing on applied math/mathematical physics, or is it pretty much going to be covered by multivariable calculus + topics from tensor analysis? To be more precise, let me reformulate the question.
If we were to draw an Euler-Venn diagram with three main circles corresponding to Multivariable Calculus, Matrix Calculus, and Tensor Analysis, then what would be the topics lying in the
- intersection of Multivariable Calculus circle and Matrix Calculus circle?
- intersection of Tensor Analysis circle and Matrix Calculus circle?
- Matrix Calculus circle, and not in any other circle?
Thank you for advice.