Matrix Definition and 1000 Threads

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.

View More On Wikipedia.org
Recent contents Top users
  1. Jamister

    I Proof about a positive definite matrix

    I need to prove the following: A symmetric real matrix ##A## with positive elements ##a_{i,j}\geq 0## can’t be definite positive matrix (i.e. with only positive eigenvalues) if the following condition holds: $$\sum_{i=1}^{N-1}a_{i,i+1}>\frac{1}{2}\sum_{i=1}^{N}a_{i,i}=\frac{1}{2}\text{Tr}(A)$$...
  2. H

    I How can I convince myself that I can find the inverse of this matrix?

    If I have a ##n\times n## matrix $$ U= \begin{bmatrix} u_{11} & u_{12} &u_{13} & \cdots u_{1n} \\ 0 & u_{22} & u_{23} & \cdots u_{2n} \\ 0&0 &u_{33} &\cdots u_{3n}\\ \vdots & \vdots &\vdots & \cdots \vdots \\ 0 & 0 & 0 &\cdots u_{nn} \end{bmatrix} $$ Now, I don't want to use the fact that it's...
  3. murshid_islam

    I Matrix representation for closed-form expression for Fibonacci numbers

    From the wikipedia page for Fibonacci numbers, I got that the matrix representation for closed-form expression for Fibonacci numbers is: \begin{pmatrix} 1 & 1 \\ 1 & 0\\ \end{pmatrix} ^ n = \begin{pmatrix} F_{n+1} & F_n \\ F_n & F_{n-1}\\ \end{pmatrix} That only works...
  4. GingFritz

    How determine that a matrix is a tensor?

    I have the matrix $$ A = \left(\begin{array}{cc} y^2 & -xy\\ -xy & x^2 \end{array} \right) $$ I know that to prove that the matrix is a tensor, it transform their elements in another base. But I still without how begin this problem. Help please! Thanks.
  5. TheScienceAlliance

    MHB Does Commutativity Hold for Matrices A and B with a Specific Matrix C?

    If A and B are matrices that AC = AC and BC=CB, where C is a matrix whose first row's entries are 0 1 and the second row's entries are -1 0, then AB=BA.
  6. Salmone

    I Matrix element in problem with hydrogen atom

    I have a problem in calculate a matrix element in a problem with hydrogen atom. I have an hydrogen atom and Hamiltonian eigenstates ##|n,l,m>## where ##n## are energy quantum numbers, ##l## are ##L^2## quantum numbers and ##m## are ##L_z## quantum numbers, I have to calculate the matrix element...
  7. M

    Is result of vector inner product retained after matrix multiplication?

    Hi, I was thinking about the following problem, but I couldn't think of any conclusive reasons to support my idea. Question: Let us imagine that we have two vectors ## \vec{a} ## and ## \vec{b} ## and they point in similar directions, such that the inner-product is evaluated to be a +ve...
  8. Rlwe

    I Determinant of a specific, symmetric Toeplitz matrix

    Let us define matrix ##\mathbf{B}_n=[b_{ij}]_{n\times n}## as follows $$[b_{ij}]_{n\times n}:=\begin{cases} b_{ij} = \alpha\,,\quad j=i\\ b_{ij}=\beta\,,\quad j=i\pm1\\ b_{ij}=1\,,\quad \text{else}\end{cases}\,,$$ where ##\alpha\,,\beta\in\mathbb{R}## and ##n\geq2##. ##\mathbf{B}_4##, for...
  9. J

    The infinite limits of the probability transition matrix for Markov chain

    Consider a Markov chain with state space {1, 2, 3, 4} and transition matrix P given below: Now, I have already figured out the solutions for parts a,b and c. However, I don't know how to go about solving part d? I mean the question says we can't use higher powers of matrices to justify our...
  10. P

    Question about hollow matrix and diagonalization

    A quick and simple question. I just realized that this has been posted in the wrong section, but ill give it a try anyway. Does anyone know if it's possible to diagonalize a hollow matrix? What i mean by a hollow matrix is a matrix with only zero entries along the diagonal.
  11. Arquimedes

    A Schmidt decomposition - How do I find the matrix related to the state?

    Hello, I am currently studying the Schmidt decomposition and how to use it to determine if a state is entangled or not and I can't understand how to write the state as a matrix so I can apply the Singular Value Decomposition and find the Schmidt coefficients. The exercise I am trying to complete...
  12. P

    Spin matrix representation in any arbitrary direction

    I've tried to use the 1st equation as a matrix to determine, but it clearly isn't a diagonal matrix. My guess is that I need to find the spin matrix along the direction ##\hat{n}##, but do I need to find the eigenstates of ##\sigma \cdot \hat{n}## first and check if they form a diagonal matrix...
  13. T

    B Does this kind of square matrix exist?

    I had a homework question that gives A as an arbitrary matrix. Then the question states that A^2=A Now I manipulate the equation to give this A^2-A=0. -->A(A-I)= 0 So A can be I or 0 Are there any other values A can take?
  14. H

    Find the basis so that the matrix will be diagonal

    First of all, it is clear that we can find such a bases (the theorem is given in almost all of the books, but if you want to share some insight I shall be highly grateful.) We can show that ##W## will be the set of all real polynomials with degree ##\leq 2##. So, let's have ##\{1,x,x^2\}## as...
  15. S

    Comp Sci I can't get this task right regarding a simple ' 2D game' as a matrix

    I have also put some notes on what is to be done in the problematic function Note also that this is not homework, but am just preparing for an exam. Thanks in advance! forgot to provide the code here, so here it is: # RPG subsystem: check whether the next player move on a 5x5 tileset is...
  16. Eclair_de_XII

    B Determinant of a transposed matrix

    By definition, ##\det A=\sum_{p_j\in P}\textrm{sgn}(p_j)\cdot a_{1j_1}\cdot\ldots\cdot a_{nj_n}##, where ##P## denotes the set of all permutations of the ordered sequence ##(1,\ldots,n)##. Denote the number of permutations needed to map the natural ordering to ##p_j## as ##N_j##. Now consider...
  17. J

    Very High Standard Deviation in Excitation Emission Matrix Measurement

    Hi, I obtain really high standard deviations in Excitation-Emission Spectra mainly for the phenolic compounds in olive oil (Em: 290-350nm). Method: I weigh 0.05g of olive oil and dilute it up to 25ml with cyclohexane to remain in the range of linearity for absorbance measurements to correct...
  18. Eclair_de_XII

    Python I'm not able to write a script that reduces a matrix to RREF in Python

    Summary:: I'm not asking for help, but I'm asking for an opinion. Is this a sign that I probably should not be pursuing a career in software development or computer science? I basically feel like this in general wrt any subject I am studying, really, whenever I feel stumped on a given problem...
  19. B

    A Calculating the Modal Matrix for A

    Mentor note: The Tex shown below had to be modified a fair amount to conform to the MathJax on this site. Trying to calculate the modal matrix for the following ##A =\begin{pmatrix} 1 && 1/2 && 1/2 \\ 0 && 1/2 && -1/2 \\ 0 && 1/2 && 1 .5 \end{pmatrix}## there are two eigenvectors for this...
  20. D

    I Usage of First Order Elastic Constants in Soft Body Equations

    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...
  21. K

    A Why is this matrix symmetric here?

    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...
  22. curiousPep

    I Resolve moment of inertia at an angle

    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...
  23. H

    Matrix with a bounded mapping as an entry is bounded

    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}...
  24. P

    A Re-writing the geodesic deviation eqn in matrix notation (3d only)

    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...
  25. fluidistic

    I How to "think" of a polarizer in matrix representation?

    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...
  26. K

    A Ambiguity in sense of rotation given a rotation matrix A

    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...
  27. K

    A Rotation matrix and rotation of coordinate system

    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...
  28. H

    I Interferences (with diagonal density matrix)

    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...
  29. K

    A Matrix proof of Euler's theorem of rotation

    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"...
  30. A

    Solving a system of differential equations by fundamental matrix

    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...
  31. I

    MHB Matrix Transforms: nxm, n->m, m->n, n+m->n/m

    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
  32. LukasMont

    Proving A Must Be of Rank 2: The 2x2 Matrix Dilemma

    My trouble is being to show A must be of rank 2. Any ideas?
  33. BWV

    Negative eigenvalues in covariance matrix

    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'...
  34. R

    Finding the transformation of a matrix

    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##...
  35. R

    Finding roots and complex roots of a determinant

    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...
  36. Poetria

    Matrix Function - Check Understanding

    I would say that what this matrix does is rotate e.g. a vector by ##\pi/2## clockwise. Am I right? I would like to check my understanding.
  37. Eclair_de_XII

    B Any square matrix can be expressed as the sum of anti/symmetric matrices

    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...
  38. B

    MHB Solve System Using Matrix Inverse

  39. Glenn Rowe

    A Simple S matrix example in Coleman's lectures on QFT

    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...
  40. L

    I Prove that the limit of this matrix expression is 0

    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...
  41. M

    MHB QR decomposition with permutation matrix

    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:
  42. N

    I How Is the Dynamical Matrix Used to Calculate the Phonon Spectrum of Graphene?

    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!
  43. B

    Troubleshooting Matrix File Uploads: Why Am I Getting Zeros?

    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) {...
  44. M

    MHB Is the Matrix A Diagonalizable with Real Eigenvalues?

    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)...
  45. T

    A Lie Bracket * Matrix * vector (Need proof)

    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...
  46. patric44

    I Dimension of a Linear Transformation Matrix

    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...
  47. F

    MATLAB Can I calculate the covariance matrix of a large set of data?

    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...
  48. T

    I Un-skewing a skew symmetric matrix (for want of a better phrase)

    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...
  49. I

    What size is the Global Stiffness Matrix in this Example?

    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
  50. S

    Determining value of r that makes the matrix linearly dependent

    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...
Back
Top