- #1
Leo321
- 38
- 0
I try to understand how to calculate derivatives of functions, which contain matrices.
For a start I am looking at derivatives by a single variable.
I have x=f(t) and I want to calculate [tex]\frac{dx}{dt}[/tex]. The caveat is that f contains matrices, that depend on t. Can I use the ordinary chain rule and product rule, and if not, then what can I use?
What for example would be [tex]\frac{d}{dt}Tr(M^kA)[/tex]? Assume M is a function of t and A is constant. Would it be [tex]kTr(M^{k-1}\frac{dM}{dt}A)[/tex], like it would have been for a scalar?
For a start I am looking at derivatives by a single variable.
I have x=f(t) and I want to calculate [tex]\frac{dx}{dt}[/tex]. The caveat is that f contains matrices, that depend on t. Can I use the ordinary chain rule and product rule, and if not, then what can I use?
What for example would be [tex]\frac{d}{dt}Tr(M^kA)[/tex]? Assume M is a function of t and A is constant. Would it be [tex]kTr(M^{k-1}\frac{dM}{dt}A)[/tex], like it would have been for a scalar?