# Tag Info

• 27.5k

### Why does the matrix exponential $e^A$ always exist?

It is worth to treat the matrix $A$ as a linear bounded operator $\mathcal{L}(\mathbb{R}^n,\mathbb{R}^n)$. Therefore defining the operator $\exp A:\mathbb{R}^n\to \mathbb{R}^n$ as a limit of the ...

### Derivative of the inverse of a symmetric matrix w.r.t itself

In the single-variable case, we have that $$\dfrac{d}{dt}C(t)^{-1}=-C(t)^{-1}\dfrac{dC(t)}{dt}C(t)^{-1}.$$ This can obtained by differentiating the expression $C(t)C(t)^{-1}=I$ on both sides with some ...
• 3,100

• 27.5k
1 vote

• 1,919
1 vote

### How to take the derivative of a matrix with respect to itself?

The answer is a lot easier than the previous posters are indicating $\frac{d}{dX}(A*X)=A$ define $A=I_m$ where $m$ is the number of rows of $X$ because $I_m*X=X$ this is an identity and you get your ...
• 31

Only top scored, non community-wiki answers of a minimum length are eligible