# Tagged Questions

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### Differentiation involving determinant

This question has arisen by following the proof in the appendix of Louis Liporace's paper on maximum-likelihood estimation, where the paper concerns classes of probabilistic functions (elliptically ...
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### Acquiring $Df(\mathbf{x})$

Sorry for the probably easy and silly question, but I try to teach myself linear algebra and I am stucked at "the derivative as a matrix" part. I know how to differentiate partially and I know how ...
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### Continuity of the inverse matrix function

For a differentiation module I am taking one of the exercises (not homework) asks: Show that the set $U \subset \mathbb{R}^{n^{2}}$ of matrices $A$ with $det(A) \neq 0$ is open. Let $A^{-1}$ be the ...
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### Derivative of quadratic form w.r.t. matrix (product)

I need to show that some quadratic from: 1' A C A 1 is increasing in matrix C , where 1 is a (Kx1) vector of ones, and A and C are both (KxK) positive definite. Can I reason like this: 1) ...
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### Derivative of a Matrix to a Power

Fix a positive interger $k$ and let $F: \mathbb{R}^{n \times n} \rightarrow \mathbb{R}^{n \times n}$ be the map on $n \times n$ matrices defined by $F(A)= A^k$. Show that $F$ is differentiable at ...
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### $\frac{d(X'X)}{dX}=?$

Thanks a lot for reading my thread. I am wondering what is the derivative of $X'X$ with respect to $X$? Here $X$ is a vector/matrix, and $X'$ is the Hermitian matrix of $X$; It would be great if ...
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### Differentiation of the transpose of a vector? [closed]

Suppose $s$ is a scalar, and $x$ is a vector, how would I calculate $$\left(\frac \delta {\delta x} (x^T s)\right)$$Basically I couldn't find any reliable source letting me know how to ...
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### Derivative of matrix and vector in $\mathbf {v^TMv}$

Suppose I have a ($n\times 1$) vector $\mathbf v$ and a ($n\times n$) matrix $\mathbf M$ and I want to compute the derivative w.r.t. some $x$. Both $\mathbf v$ and $\mathbf M$ depend on the scalar ...
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### Vector derivative $\frac{d(Ax)}{d(x)}$ [closed]

I just need to know that whether it is $A$ or $A^T$ . I need it for an homework . Please be quick in telling me . Thanks !
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### Derivative of matrix inverse w.r.t. vector

I need to differentiate the inverse of the $K\times K$ symmetric matrix $A$ w.r.t some vector (that $A$ depends on). Is there a rule for this? In case I do the derivative w.r.t. to some scalar there's ...
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### Getting stonewalled on computation of $2\times 2$ Hessian matrix

The question: Let $z \in R^N$, and let $f(z) = \log[1^T z] \in R$. I am told that the Hessian matrix of this function is the following:  H = \frac{1}{1^Tz}\Big[ 1^Tz \mathrm{diag}(z) - zz^T \Big] ...
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### Differentiation of bilinear form w.r.t. matrix

I need to do a derivative of bilinear form: b'C a w.r.t to Kx1 vector t where "b" and "a" are Kx1 vectors and "C" is KxK matrix that depends on vector t (and a and b are independent of t). Does anyone ...
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### Show there is no solution…

Show that there is no solution to $(\bf D_n − I)p = 0$ except $\bf p = 0$; where $\bf D_n$ is the matrix representing the (ﬁrst) derivative for degree $n$ polynomials and $\bf p=[c_0; c_1; c_2]$ ...
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### Derivative of sqrt( Vector * Matrix * Vector ) according to one coordonate of the vector

I have a $n$ element vector $V$ and a symmetric $n\times n$ matrix $M$ (all of real elements). I calculate a score as $({ V^TMV })^{1/2}$ Now is there a formula that would give me: the derivative ...