I'm trying to do some scientific programming, but I have limited math experience. My supervisor has given me the following equation I need to solve for $d$: $$ Y = Xe^{-b\cdot d}. $$ where
- $X$ and $Y$ are $96 \times 96$ matrices,
- and $b$ and $d$ are $3\times 3$ matrices (the '$\cdot$' sing above signifies dot product).
I'm not even sure how I would go about trying to solve for $d$. It doesn't seem to make sense to rearrange the equation above to $$ d = \mathrm{inv}(b) \ln(X/Y), $$ since (1) I'm not sure how dot product works with tensors (do I need to learn dyadic algebra to do this???), but I didn't think you could just do $\mathrm{inv}(b)(b\cdot d)$. And how are you supposed to end up with a $3\times 3$ matrix if you're multiplying a $3\times 3$ matrix by a $96\times 96$ one?
If anyone could please give suggest some resources or give me some direction, I would be sincerely appreciative, and thank you for your time.