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.
Hi, I have some soft body equations that require first order elasticity constants. Just trying to figure out the proper indexing.
From Finite Elements of Nonlinear Continua by J.T. Oden, the elastic constants I am trying to obtain are the first order, circled below:
My particular constitutive...
Goldstein 3rd Ed, pg 339
"In large classes of problems, it happens that ##L_{2}## is a quadratic function of the generalized velocities and ##L_{1}## is a linear function of the same variables with the following specific functional dependencies:
##L\left(q_{i}, \dot{q}_{i}, t\right)=L_{0}(q...
Initially, I calculate the moment of inertia of of a square lamina (x-z plane). Thr this square is rotated an angle $\theta$ about a vertex and I need to calculate the new moment of inertia about that vertex.
Can I split the rotated square to two squares in the x-z plane and y-z plane to find...
In a previous exercise I have shown that for a $$C^{*} algebra \ \mathcal{A}$$ which may or may not have a unit the map $$L_{x} : \mathcal{A} \rightarrow \mathcal{A}, \ L_{x}(y)=xy$$ is bounded. I.e. $$||L_{x}||_{\infty} \leq ||x||_{1}$$, $$x=(a, \lambda) \in \mathcal{\hat{A}} = \mathcal{A}...
This is my attempt to re-write the geodesic deviation equation in the special case of 3 dimensions and +++ signature in matrix notation.
We start with assuming an orthonormal basis. Matrix notation allows one to express vectors as column vectors, and dual vectors as row vectors, but by...
From what I remember of my optics course, any element such as a lens (be it thick or thin), can be represented by a matrix. So they are sort of operators, and it is then easy to see how they transform an incident ray, since we can apply the matrix to the electric field vector and see how it gets...
Goldstein 3rd Ed pg 161.
Im not able to understand this paragraph about the ambiguity in the sense of rotation axis given the rotation matrix A, and how we ameliorate it.
Any help please.
"The prescriptions for the direction of the rotation axis and for the rotation angle are not unambiguous...
If we change the orientation of a coordinate system as shown above, (the standard eluer angles , ##x_1y_1z_1## the initial configuration and ##x_by _b z_b## the final one), then the formula for the coordinates of a vector in the new system is given by
##x'=Ax##
where...
suppose that elecrons are in a state described by a diagonal density matrix for their spin (we are not interested in their spatial matrix). They are used in the double slit experiment. will we get fringes.
I ask the question because when Bob ans Alice share pairs of electrons (the total spin of...
The question arises the way Goldstein proves Euler theorem (3rd Ed pg 150-156 ) which says:
" In three-dimensional space, any displacement of a rigid body such that
a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point"...
I am given this system of differential equations;
$$ x_1'=2t^2x_1+3t^2x_2+t^5 $$
$$ x_2' =-2t^2x_1-3t^2x_2 +t^2 $$
Now the first question states the following;
Find a fundamental matrix of the corresponding homogeneous system and
explain exactly how you arrive at independent solutions
And the...
A matrix of dimension nxm
a. transforms a vector of dimension n to a vector of dimension m
b. transforms a vector of dimension m to a vector of dimension n
c. a vector of dimension n+m to a vector of dimension m
d. a vector of dimension n+m to a vector of dimension n
Trying to run the factoran function in MATLAB on a large matrix of daily stock returns. The function requires the data to have a positive definite covariance matrix, but this data has many very small negative eigenvalues (< 10^-17), which I understand to be a floating point issue as 'real'...
I have the matrix above and I have to find which transformation is that.
##\begin{bmatrix}
cos \theta & sin \theta \\
sin \theta & -cos \theta
\end{bmatrix}##
For a vector ##\vec{v}##
##v_x' = v_x cos \theta + v_y sin \theta##
##v_y' = v_x sin \theta - v_y cos \theta##
If ##\phi##...
I need to find the values of ##\Omega## where ##(-\Omega^2 + i\gamma\Omega + \frac{2k}{3m})(-\Omega^2 + i\gamma\Omega + \frac{2k}{3m}) - (-i\gamma\Omega)(-i\gamma\Omega) = 0##
I get ##\Omega^4 -2i\gamma \Omega^3 - \frac{4k}{3m}\Omega^2 + i\frac{4k}{3m}\gamma\Omega + \frac{4k^2}{9m^2} = 0##
I...
Let ##A## be a matrix of size ##(n,n)##. Denote the entry in the i-th row and the j-th column of ##A## by ##a_{ij}##, for some ##i,j\in\mathbb{N}##. For brevity, we call ##a_{ij}## entry ##(i,j)## of ##A##.
Define the matrix ##X## to be of size ##(n,n)##, and denote entry ##(i,j)## of ##X## as...
In Coleman's QFT lectures, I'm confused by equation 7.57. To give the background, Coleman is trying to calculate the scattering matrix (S matrix) for a situation in which the Hamiltonian is given by
$$H=H_{0}+f\left(t,T,\Delta\right)H_{I}\left(t\right)$$
where ##H_{0}## is the free Hamiltonian...
Given a singular matrix ##A##, let ##B = A - tI## for small positive ##t## such that ##B## is non-singular. Prove that:
$$
\lim_{t\to 0} (\chi_A(B) + \det(B)I)B^{-1} = 0
$$
where ##\chi_A## is the characteristic polynomial of ##A##. Note that ##\lim_{t\to 0} \chi_A(B) = \chi_A(A) = 0## by...
Hey! :giggle:
At the QR-decomposition with permutation matrix is the matrix $R$ equal to $R=G_3^{-1}P_1G_2^{-1}P_0G_1^{-1}A$ or $G_3P_1G_2P_0G_1A=R$? Which is the correct one? Or are these two equivalent?
In general, it holds that $QR=PA$, right?
:unsure:
Starting on page 11 of this paper on lattice dynamics, the phonon spectrum of graphene is calculated. I do not really understand how the author used the matrix they created in order to calculate the spectrum. Thanks!
Hello everybody,
I created this tamplet to upload a file matrix:
#include <sstream>
#include "fstream"
#include <vector>
#include <iostream>
#include <string>
template<class T >std::istream& readMatrix(std::vector<std::vector<T>>& outputMatrix, std::istream& inStream)
{
if (inStream) {...
Hey! :giggle:
We consider the $4\times 4$ matrix $$A=\begin{pmatrix}0 & 1 & 1 & 0\\ a & 0 & 0 & 1\\ 0 & 0 & b & 0 \\ 0 & 0 & 0 & c\end{pmatrix}$$
(a) For $a=1, \ b=2, \ c=3$ check if $A$ is diagonalizable and find a basis of $\mathbb{R}^4$ where the elements are eigenvectors of $A$.
(b)...
As an aside, fresh_42 commented and I made an error in my post that is now fixed. His comment, below, is not valid (my fault), in that THIS post is now fixed.Assume s and w are components of vectors, both in the same frame
Assume S and W are skew symmetric matrices formed from the vector...
hi guys
I was trying to find the matrix of the following linear transformation with respect to the standard basis, which is defined as
##\phi\;M_{2}(R) \;to\;M_{2}(R)\;; \phi(A)=\mu_{2*2}*A_{2*2}## ,
where ##\mu = (1 -1;-2 2)##
and i found the matrix that corresponds to this linear...
Hello everyone. I want to calculate the covariance matrix of a stochastic process using Matlab as
cov(listOfUVValues)
being the dimensions of listOfUVValues 211302*50. I get the following error:
Requested 211302x211302 (332.7GB) array exceeds maximum array size preference. Creation of...
Hello
Say I have a column of components
v = (x, y, z).
I can create a skew symmetric matrix:
M = [0, -z, y; z, 0; -x; -y, x, 0]
I can also go the other way and convert the skew symmetric matrix into a column of components.
Silly question now...
I have, in the past, referred to this as...
does this Beam, composed of three elements and 4 nodes(considering lateral deflections and slopes) has an 8x8 global stifness matrix
and if so is the global matrix calculated the same way as a 6x6 stifness matrix for the same kind of beam but only with two elements and 3 nodes
for problem (a), all real numbers of value r will make the system linearly independent, as the system contains more vectors than entry simply by insepection.
As for problem (b), no value of r can make the system linearly dependent by insepection. I tried reducing the matrix into reduced echelon...
Hi, there. I am working with a model, in which the dimension of the Hilbert space is infinite. But Since only several states are directly coupled to the initial state and the coupling strength are weak, then I only consider a subspace spanned by these states.
The calculation shows that the...
In the 4-dimensional representation of ##\beta##, ## \beta=\begin{pmatrix}\mathbf I & \mathbf 0 \\ \mathbf0 & -\mathbf I\end{pmatrix} ,## and we can suppose ## \alpha_i=\begin{pmatrix}\mathbf A_i & \mathbf B_i \\ \mathbf C_i & \mathbf D_i\end{pmatrix} ##.
From the anti-commutation relation...
https://projecteuler.net/problem=101import numpy as np
for j in range (1,11):
M = np.empty([j, j])
for x in range(1,j+1):
for y in range(1,j+1):
M[y,x] = y**(j-x)
Minv = np.linalg.inv(M)The ##j^{\mathrm{th}}## estimate ##\mathrm{OP}(j,n)## which fits ##j## data...
The following matrix is given.
Since the diagonal matrix can be written as C= PDP^-1, I need to determine P, D, and P^-1.
The answer sheet reads that the diagonal matrix D is as follows:
I understand that a diagonal matrix contains the eigenvalues in its diagonal orientation and that there must...
Hey!
A function $f:\mathbb{R}^n\rightarrow \mathbb{R}$ is convex if for all $x,y\in \mathbb{R}^n$ the inequality $$f(tx+(1-t)y)\leq tf(x)+(1-t)f(y)$$ holds for all $t\in [0,1]$.
Show that a twice continuously differentiable funtion $f:\mathbb{R}^n\rightarrow \mathbb{R}$ is convex iff the...
Hello,
I am puzzled about the following condition. Assume a matrix A with complex-valued zero-mean Gaussian entries and a matrix B with complex-valued zero-mean Gaussian entries too (which are mutually independent of the entries of matrix A).
Then, how can we prove that...
My guess is that since there are no rows in a form of [0000b], the system is consistent (the system has a solution).
As the first column is all 0s, x1 would be a free variable.
Because the system with free variable have infinite solution, the solution is not unique.
In this way, the matrix is...
Hi,
I'm using Scientific Workplace to write LaTex and it generates the code shown below for the given matrix. I don't think the generated code is standard LaTex in this particular instance. How can I fix it without making too many modifications? I mean if there is a simple way to fix it. Thank...
hello
matrix and wave formulation of QM are equivalent theories i.e they yield the same results
Which one is most frequentely used by professional scientists in solving real problems and why ?
I have taken the variables as follows:
A[][]=the matrix
max=to store the maximum integer value present in the matrix
min=to store the minimum integer value present in the matrix
sum=to store the sum of boundary elements
display()=methos to print matrix
sort()=method to sort matrix in descending...
Good afternoon to all again! I'm solving last year's problems and can't cope with this problem:( help me to understand the problem and find a solution!
good evening everyone!
Decided to solve the problems from last year's exams. I came across this example. Honestly, I didn't understand it. Who can help a young student? :)
Find characteristic equation of the matrix A in the form of the polynomial of degree of 3 (you do not need to find...
Gonna preface by saying I never thought linear algebra would be a class I would regret not taking so much... but in short the goal is to reduce an arbitrary symmetric NxN system using a set of auxiliary constraint relationships, e.g. for a 3x3
\begin{bmatrix}
V_1\\
V_2\\
V_3\\
\end{bmatrix}
=...
In a 2012 article published in the Mathematical Gazette, in the game of golf hole score probability distributions were derived for a par three, four and five based on Hardy's ideas of how an hole score comes about. Hardy (1945) assumed that there are three types of strokes: a good (##G##)...
Hello,
Let's consider a vector ##X## in 2D with its two components ##(x_1 , x_2)_A## expressed in the basis ##A##. A basis is a set of two independent (unit or not) vectors. Any vector in the 2D space can be expressed as a linear combination of the two basis vectors in the chosen basis. There...
I try to solve but i have 1 step in the solution that I don't understand who to solve.
Below in the attach files you can see my solution, the step that I didn't make to prove Marked with a question mark.
thanks for your helps (:
Hi,
I was trying to do the following problem. I was able to do the part in pink highlight (please check "My attempt") but the part in orange highlight makes no sense to me. I'd really appreciate if you could help me to solve the part in orange. Thank you!
My attempt:
The solution presented...
$$\langle p | W | p' \rangle = \int \langle p | x \rangle \langle x W | x' \rangle \langle x' p' \rangle dx dx'$$
$$\langle p | W | p' \rangle = \int \langle p | x \rangle \delta(x-x') W(x) \langle x' | p' \rangle dx dx'$$
$$\langle p | W | p' \rangle = \int \langle p | x' \rangle W(x') \langle...