Tagged Questions
4
votes
1answer
43 views
derivative of log(det(A)) wrt x, where A is matrix that depends on x
I have two large sparse matrices B and C, and I need to calculate
$\frac{\rm{d}}{\rm{d}(\log({\lambda}) }\log( \det(B+\lambda C))$.
Because B and C are very large I can't directly evaluate the ...
1
vote
1answer
44 views
Gradient of a scalar function with respect to a matrix
I need to calculate $\dfrac{\partial}{\partial K}f(K)$, with:
$$
f(K)=-\frac{1}{2}(u-Kx)^T\Sigma^{-1}(u-Kx)$$
$K$ and $\Sigma$ are $n\times n$ matrices, $\Sigma$ is symmetric, $u$ and $x$ are column ...
0
votes
1answer
17 views
Extremum of a multidimensional quadratic function
I have the following function:
$$
g(h) = h'\Sigma\Sigma'h-h'm-r,
$$
where $h$ is a vector in $\mathbb{R}^M$, $\Sigma$ is a $M\times K$ matrix such that $\Sigma\Sigma'$ is positive definite and has ...
3
votes
2answers
52 views
Formula for Nth Derivative of Matrix Inverse
I was looking for an equation for the nth derivative of a matrix inverse, ie
$\frac{d^n \bf{A}^{-1}}{dx^n}$
I know that the first derivative
$\frac{\text{d} \bf{A}^{-1}}{\text{d}x} = -\bf{A}^{-1} ...
0
votes
0answers
44 views
Matrix differentiation.
Given $A$ is square matrix depends on a scalar $x$, is there rules to find $df(a)/dx$? For example, indices rule or chain rule? I found this kind of information is not much on the internet. Thanks.
1
vote
1answer
41 views
Study of Matrix Calculus
I need to study matrix calculus such as integration, differentiation, differentiation of functions of determinants and inverse matrices and then also other matrix based calculations such as ...
1
vote
1answer
59 views
On the existence of a notation in matrix calculus
Is there any especial operator on the function $f(x)$ to represent the following matrix:
\begin{bmatrix}
f & \frac{\mathrm{d}}{\mathrm{d} x}f & \frac{\mathrm{d^2}}{\mathrm{d} x^2}f & ... ...
6
votes
1answer
86 views
Integrals of matrix functions
I've stumbled across some math I've never really encountered before, and I would love it if someone could provide me with some useful references and texts on it. I'm dealing with integration over the ...
1
vote
0answers
34 views
Matrix functions via Cauchy integral
I shall be much obliged if one provides me with references on calculation of "standard" matrix functions by use of Cauchy integral, such as
matrix exponent
matrix logarithm
matrix square root
matrix ...
3
votes
1answer
66 views
Polynomial roots or discriminant
I was wondering if it is possible to find the roots of the following polynomial
$$
P(x)=x^n+ax^m+b
$$
or at least can I get the discriminant of it, which is the determinant of the Sylvester matrix ...
0
votes
1answer
52 views
Calculating Log-likelihood using Raphson and Jacobian matrices?
I am reading the following paper:
http://www.ntuzov.com/Nik_Site/Niks_files/Research/papers/stat_arb/Ahmed_2009.pdf
and in particular page 13. I want to try and calculate lambda_t(p) = exp^(Beta^T ...
0
votes
0answers
38 views
Differentiating an expression with matrices and determinants
I have the following function:
$$f(\sigma_n^2,l,\sigma_f^2) = -\frac{1}{2} y^T \left(\mathbf{K}+\sigma_n^2\mathbf{I} \right)^{-1}y - \frac{1}{2} \log \left| \mathbf{K}+\sigma_n^2\mathbf{I} \right| - ...
2
votes
1answer
163 views
Derivative of matrix involving trace and log
I'm stuck on this problem.
Let $X\in\mathbb{R}^{n\times n}$, compute the following matrix derivatives
$$\frac{\partial}{\partial X}\mathrm{tr}(\log(XA)\log(XA)^\top),$$
$$\frac{\partial}{\partial ...
0
votes
0answers
56 views
Is this function involving matrices convex?
Let $X\in \mathbb{R}^{n \times n}$.
Then, is the function
$$ \text{Tr}\left( (X^T X )^{-1} \right)$$
convex in $X$? ($\text{Tr}$ denotes the trace operator)
4
votes
1answer
73 views
How to calculate this $\frac{0}{0}$ limit?
Let $R=\left[\begin{array}{ccc}
\frac{1}{2} & \frac{1}{2} & 0\\
\frac{1}{3} & \frac{1}{3} & \frac{1}{3}\\
0 & 0 & 1
\end{array}\right]$, $P=\left[\begin{array}{ccc}
...
