The Multistate Anti-Terrorism Information Exchange Program, also known by the acronym MATRIX, was a U.S. federally funded data mining system originally developed for the Florida Department of Law Enforcement described as a tool to identify terrorist subjects.
The system was reported to analyze government and commercial databases to find associations between suspects or to discover locations of or completely new "suspects". The database and technologies used in the system were housed by Seisint, a Florida-based company since acquired by Lexis Nexis.
The Matrix program was shut down in June 2005 after federal funding was cut in the wake of public concerns over privacy and state surveillance.
Hello everyone,
A simple ring resonator with a bus waveguide is described by:
$$ \begin{pmatrix} E_{t1}\\ E_{t2} \end{pmatrix} =
\begin{pmatrix} t & k\\ -k^* & t^* \end{pmatrix}
\begin{pmatrix} E_{i1}\\ E_{i2} \end{pmatrix} $$
I do not understand though why we have -k* and t*? Shouldn't...
For part (b) i was able to use equations to determine the eigenvectors;
For example for ##λ =6##
##12x +5y -11z=0##
##8x-4z=0##
##32x+10y-26z=0## to give me the eigen vector,
##\begin{pmatrix}
1 \\
2 \\
2
\end{pmatrix}## and so on.
My question is to get matrix P does the arrangement of...
I hope this is more properly laid out?
We previously established that the stationery points were (1,1) and (-1,1)
For this first stage I now need to create the elements of a Jacobian maitrix using partial differentation.
I am confused by reference to the chain rule.
Am I correct that for dx/dt...
Please confirm or deny the correctness of my understanding about this definition.
For a given set of ##t_i##s, the matrix ##(B(t_i,t_j))^k_{i,j=1}## is a constant ##k\times k## matrix, whose entries are given by ##B(t_i,t_j)## for each ##i## and ##j##.
The the 'finite' in the last line of the...
I have never solved a matrix ODE before, and am wondering if solving it is similar to solving ##y'=ay## where ##a## is a constant and ##y:\mathbb{R} \longrightarrow \mathbb{R}## is a function. The solution is right according to wikipedia, and I am just looking for your inputs. Thanks...
Let X be a continuous-time Markov chain that hops between two states ##\{1, 2\}## with rates ##\lambda, \mu>0##, so its generator is
$$Q = \begin{pmatrix}
-\mu & \mu\\
\lambda & -\lambda
\end{pmatrix}.$$
Solve ##\pi Q = 0## for the stationary distribution, and verify that...
I have the matrix relationship $$C = A^{-1} B^{-1} A B$$ I want to solve for ##A##, where ##A, B, C## are 4x4 homogeneous matrices, e.g. for ##A## the structure is $$A = \begin{pmatrix} R_A & \delta_A \\ 0 & 1 \end{pmatrix}, A^{-1} =\begin{pmatrix} R_A^\intercal & -R_A^\intercal\delta_A \\ 0 & 1...
I tried to find the answer to this but so far no luck. I have been thinking of the following:
I generate two random vectors of the same length and assign one of them as the right eigenvector and the other as the left eigenvector.
Can I be sure a matrix exists that has those eigenvectors?
I am struggling to rederive equations (61) and (62) from the following paper, namely I just want to understand how they evaluated terms like ##\alpha\epsilon\alpha^{T}## using (58). It seems like they don't explicitly solve for ##\alpha## right?
hi, we have learned that after modelling Lagrangian and extracting Feynman rules from it - we can find matrix element - from which decay width can be calculated - and than Branching ratio - my question is can we use some other way of calculatiing BR , or can we use our Lagrangain in our Euler...
Hello everyone.
I have four thermometers which measure the temperature in four different positions. The data is distributed as a matrix, where each column is a sensor, and each row is a measurement. All measurements are made at exactly the same times, one measurement each hour. I have...
The trace of the sigma should be the same in both new and old basis. But I get a different one. Really appreciate for the help.
I’ll put the screen shot in the comment part
Can somebody explain why the kinetic term for the fluctuations was already diagonal and why to normalize it, the sqrt(m) is added? Any why here Z_ij = delta_ij?
Quite confused about understanding this paragraph, can anybody explain it more easily?
Suppose ##A## and ##B## are positive definite complex ##n \times n## matrices. Let ##M## be an arbitrary complex ##n \times n## matrix. Show that the block matrix ##\begin{pmatrix} A & M\\ M^* & B\end{pmatrix}## is positive definite if and only if ##M = A^{1/2}CB^{1/2}## for some matrix ##C## of...
It would be nice if someone could find the history of why we use the letters i and j or m and n for the basics when working with Matrices ( A = [aij]mxn ). I tried looking up the information and I was not successful. I understand what they represent in the context of the matter, but not why they...
A blog post by Evan Chen https://blog.evanchen.cc/2016/07/12/the-structure-theorem-over-pids/ says that elementary row and column operations on a matrix can be interpreted as a change-of-basis.
I assume this use of the phrase "change of-basis" refers to creating a matrix that uses a different...
Let ##A## be a complex nilpotent ##n\times n##-matrix. Show that there is a unique nilpotent solution to the quadratic equation ##X^2 + 2X = A## in ##M_n(\mathbb{C})##, and write the solution explicitly (that is, in terms of ##A##).
Every hermitian matrix is unitary diagonalizable. My question is it possible in some particular case to take hermitian matrix ##A## that is not diagonal and diagonalize it
UAU=D
but if ##U## is not matrix that consists of eigenvectors of matrix ##A##. ##D## is diagonal matrix.
The sigma tensor composed of the commutator of gamma matrices is said to be able to represent any anti-symmetric tensor.
\sigma_{\mu\nu} = i/2 [\gamma_\mu,\gamma_\nu]
However, it is not clear how one can arrive at something like the electromagnetic tensor.
F_{\mu\nu} = a \bar{\psi}...
For this,
What was wrong with the notation I used for showing that I has swapped the rows? The marker put a purple ?
Any help greatly appreciated!
Many thanks!
I found a the answer in a script from a couple years ago. It says the kinetic energy is
$$
T = \frac{1}{2} m (\dot{\vec{x}}^\prime)^2 = \frac{1}{2} m \left[ \dot{\vec{x}} + \vec{\omega} \times (\vec{a} + \vec{x}) \right]^2
$$
However, it doesn't show the rotation matrix ##R##. This would imply...
For this problem,
Find ##A^{-1}## given,
The solution is,
However, in the first image, why are we allowed to put together the submatrices in random order? In general does someone please know why we are allowed to decompose matrices like this?
Many thanks!
For,
Does anybody please know why they did not change the order in the second line of the proof? For example, why did they not rearrange the order to be ##M^n = (DP^{-1}P)(DP^{-1}P)(DP^{-1}P)(DP^{-1}P)---(DP^{-1}P)## for to get ##M^n = (DI)(DI)(DI)(DI)---(DI) = D^n##
Many thanks!
For this,
Dose someone please know where they get P and D from?
Also for ##M^k##, why did they only raise the the 2nd matrix to the power of k?
Many thanks!
The published solutions indicate that the nullspace is a plane in R^n. Why isn't the nullspace an n-1 dimensional space within R^n? For example, if I understand things correctly, the 1x2 matrix [1 2] would have a nullspace represented by any linear combination of the vector (-2,1), which...
In https://www.math.drexel.edu/~tolya/derivative, the author selects a domain P_2 = the set of all coefficients (a,b,c) (I'm writing horizontally instead off vertically) of second degree polynomials ax^2+bx+c, then defines the operator as matrix
to correspond to the d/dx linear transformation...
My answer:
Then, if I am not mistaken, the solution made in that video is mostly guessing about which columns combination can be equals to zero
and I found 1st, 2nd, and 3rd rows as well as 2nd, 3rd, 4th rows are equals to zero so the minimum hamming distance is 3 since my answer is mostly...
Since ##AB = B##, so matrix ##A## is an identity matrix.
Similarly, since ##BA = A## so matrix ##B## is an identity matrix.
Also, we can say that ##A^2 = AA=IA= A## and ##B^2 = BB=IB= B##.
Therefore, ##A^2 + B^2 = A + B## which means (a) is a correct answer.
Also we can say that ##A^2 + B^2 =...
I feel if we have the matrix equation X = AB, where X,A and B are matrices of the same order, then if we apply an elementary row operation to X on LHS, then we must apply the same elementary row operation to the matrix C = AB on the RHS and this makes sense to me. But the book says, that we...
Let ##M## be a nonzero complex ##n\times n##-matrix. Prove $$\operatorname{rank}M \ge |\operatorname{trace} M|^2/\operatorname{trace}(M^\dagger M)$$ What is a necessary and sufficient condition for equality?
For this,
I am not sure what the '2nd and 5th the variables' are. Dose someone please know whether the free variables ##2, 0, 0## from the second column and ##5, 8, \pi##? Or are there only allowed to be one free variable for each column so ##2## and ##5## for the respective columns.
Also...
Since Ax = b has no solution, this means rank (A) < m.
Since ##A^T y=c## has exactly one solution, this means rank (##A^T##) = m
Since rank (A) ##\neq## rank (##A^T##) so matrix A can not exist. Is this valid reasoning?
Thanks
My attempt:
$$
\begin{vmatrix}
1-\lambda & b\\
b & a-\lambda
\end{vmatrix}
=0$$
$$(1-\lambda)(a-\lambda)-b^2=0$$
$$a-\lambda-a\lambda+\lambda^2-b^2=0$$
$$\lambda^2+(-1-a)\lambda +a-b^2=0$$
The value of ##\lambda## will be positive if D < 0, so
$$(-1-a)^2-4(a-b^2)<0$$
$$1+2a+a^2-4a+4b^2<0$$...
Hi! Please, could you help me on how to solve the following matrix ?
I need to replace the value 3 on the third line by 0, the first column need to remain zero and 1 for the third column. I'm having a lot of difficulties with this. How would you proceed ?
Thank you for your time and help...
The attempt at a solution:
I tried the normal method to find the determinant equal to 2j. I ended up with:
2j = -4yj -2xj -2j -x +y
then I tried to see if I had to factorize with j so I didn't turn the j^2 into -1 and ended up with 2 different options:
1) 0= y(-4j-j^2) -x(2j-1) -2j
2)...
It is easy to see that a matrix of the given form is actually an unitary matrix i,e, satisfying AA^*=I with determinant 1. But, how to see that an unitary matrix can be represented in the given way?
Let ## \mathbf{x''} = A\mathbf{x} ## be a homogenous second order system of linear differential equations where
##
A = \begin{bmatrix}
a & b\\
c & d
\end{bmatrix}
## and ##
\mathbf{x} = \begin{bmatrix}
x(t)\\ y(t))
\end{bmatrix}
##
Now to solve this equation we transform it into a 4x4...
How to derive (proof) the following
trace(A*Diag(B*B^T)*A^T) = norm(W,2),
where W = vec(sqrt(diag(A^T*A))*B)
&
sqrt(diag(A^T*A)) is the square root of diag(A^T*A),
B & A are matrix.
Please see the equation 70 and 71 on page 2068 of the supporting matrial.
Hi all,
I want to know if a second solution exists for the following math equation:
Ce^{At} ρ_p+(CA)^{−1} (e^{At}−I)B=0
Where C, ρ_p, A and B are constant matrices, 't' is scalar variable. I know that atleast one solution i.e. 〖t=θ〗_1 exists, but I want a method to determine if there is...
In a permutation matrix (the identity matrix with rows possibly rearranged), it is easy to spot those rows which will indicate a fixed point -- the one on the diagonal -- and to spot the pairs of rows that will indicate a transposition: a pair of ones on a backward diagonal, i.e., where the...
TL;DR Summary: For every Complex matrix proove that: (Y^*) * X = complex conjugate of {(X^*) * Y}
Here (Y^*) and (X^*) is equal to complex conjugate of (Y^T) and complex conjugate of (X^T) where T presents transponse of matrix
I think we need to use (A*B)^T= (B^T) * (A^T) and
Can you help...
Until now in my studies - matrices were indexed like ##M_{ij}##, where ##i## represents row number and ##j## is the column number. But now I'm studying vectors, dual vectors, contra- and co-variance, change of basis matrices, tensors, etc. - and things are a bit trickier.
Let's say I choose to...