# Tagged Questions

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### The derivative of matrix vector product with respect to matrix

Given function $$f(M) = Mv$$ where $M$ has dimension $n \times n$, and $v$ is a vector with dimension $n \times 1$. What's the derivative of $f(M)$ with respect to $M$?
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### Why is this proof valid - inverse function theorem

Question from worksheet, I don't fully understand the solution the teacher gave. Question: let $S$ be the set of symmetric positive definite matrices of dimension $n$x$n$. Let $T: S \to S$, ...
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### Find the differential of $f(A)=det(A^{-1}-A)$ where $A$ is invertible.

The question is if $A$ is an invertible matrix with real entries of size $n$. Is $f(A)=det(A^{-1}-A)$ differentiable? and what is the differential. I think I managed to show it's differentiable. the ...
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### Gradient of matrix exponential function

Grateful if somebody could help me with the following. I am trying to find the gradient of the next expression: $$f(a_1, a_2, a_3, a_4)=\Vert R*y-x \Vert$$ where $y$ and $x$ are known 4x1 column ...
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### How to compute time ordered Exponential?

So say you have a matrix dependent on a variable t: $$A(t)$$ how do you compute $$e^{A(t)}$$ It seems Sylvester's formula, my standard method of computing matrix exponentials can't be applied ...
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### Proving a set of $2\times 3$ matrices is a manifold?

The way I have always been told to check if something is a manifold (I haven't had a whole lot of experience with them), is to check if the derivative of the function representing the loci of the ...
### Derivative of a function of a matrix $f(B) = x^T(AB)^ky$
I have a function of the form $f(B) = x^T(AB)^ky$ where $x$ and $y$ are column matrices, $A$ and $B$ are square matrices, and $B$ is a diagonal matrix, and $k$ is an integer constant. I want to find ...