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.

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  1. S

    Matrix of a Linear Transformation Example

    Homework Statement Hi this isn't really a question but more so understanding an example that was given to me that I not know how it came to it's conclusion. This is a question pertaining linear transformation for coordinate isomorphism between basis. https://imgur.com/a/UwuACHomework Equations...
  2. Martin V.

    Understanding the Role of Matrix Multiplication in Solving Equations

    Hello hope you can help me. Can anybody tell me what goes on from equation 3 to 4. especially how gets in?
  3. RJLiberator

    Inner product propety with Scalar Matrix (Proof)

    Homework Statement Let A be an nxn matrix, and let |v>, |w> ∈ℂ. Prove that (A|v>)*|w> = |v>*(A†|w>) † = hermitian conjugate Homework EquationsThe Attempt at a Solution Struggling to start this one. I'm sure this one is likely relatively quick and painless, but I need to identify the trick...
  4. D

    Diagonalizing a Matrix: Steps and Verification

    Homework Statement Diagonalize matrix using only row/column switching; multiplying row/column by a scalar; adding a row/column, multiplied by some polynomial, to another row/column. Homework EquationsThe Attempt at a Solution After diagonalization I get a diagonal matrix that looks like...
  5. Corwin_S

    What is the Jones Matrix of a mirror at an angle?

    Hi, Concerning optical polarization, what is the Jones Matrix of a mirror at a non-zero angle of incidence with respect to incoming light? For a mirror at normal incidence the matrix is (1 0; 0 -1); How do I incorporate the angle?
  6. TheSodesa

    Finding the eigenvectors of a matrix A

    Homework Statement A = \begin{bmatrix} 2 & 1 & 0\\ 0& -2 & 1\\ 0 & 0 & 1 \end{bmatrix} Homework EquationsThe Attempt at a Solution The spectrum of A is \sigma (A) = { \lambda _1, \lambda _2, \lambda _3 } = {2, -2, 1 } I was able to calculate vectors v_1 and v_3 correctly out of the...
  7. C

    How many hadamard matrix matrices exists for size n?

    Homework Statement How many hadamard matrices exists for size n? Homework Equations Hadamard matrices are square matrices whose entries are either +1 or −1 and whose rows are mutually orthogonal. The Attempt at a Solution I am just curious how many exists for 4, 8 and in general.[/B]
  8. piJohn1411

    Mathematica Is it possible to colour the rows or columns of a matrix?

    Hi, I was wondering if it's possible to colour the rows and columns of a matrix in mathematica. I have received help from another forum and the code of my matrix is the following: Rasterize@ Style[MatrixForm[{{n, -1 + n, -2 + n, \[CenterEllipsis], 1}, {2 n, 2 n - 1, 2 n - 2...
  9. Amith2006

    Quark mixing factor in CKM matrix

    I find that the quark mixing factor say for example ##V_{ub}## is the same for: u ##\Leftrightarrow## b ##u\Leftrightarrow\bar{b}## ##\bar{u}\Leftrightarrow## b ##\bar{u}\Leftrightarrow\bar{b}## Does this have something to do with weak interaction being unable to distinguish these from one...
  10. kostoglotov

    Backwards difference matrix divided by negative delta x?

    An exercise in my text requires me to (in MATLAB) generate a numeric solution to a given second order differential equation in three different ways using a forwards, centered and backwards difference matrix. I got reasonable answers for \vec{u} that agreed with each other (approximately) for the...
  11. N

    Do Both HHH and HHH Follow the Same Complex Wishart Distribution?

    Hello, Assume that H is a n \times m matrix with i.i.d. complex Gaussian entries each with zero mean and variance \sigma. Also, let n>=m. I ' m interested in finding the relation between the distribution of HHH and HHH, where H stands for the Hermittian transposition. I anticipate that both...
  12. ognik

    MHB Exploring the 3-D Rotation Matrix with Euler Rotations and Net Angle of Rotation

    The question mentions an orthogonal matrix describing a rotation in 3D ... where $\phi$ is the net angle of rotation about a fixed single axis. I know of the 3 Euler rotations, is this one of them, arbitrary, or is there a general 3-D rotation matrix in one angle? If I build one, I would start...
  13. N

    Relation between Gram matrix distributions

    Hello, Assume that H is a n \times m matrix with i.i.d. complex Gaussian entries each with zero mean and variance \sigma. Also, let n>=m. I ' m interested in finding the relation between the distribution of HHH and HHH, where H stands for the Hermittian transposition. I anticipate that both...
  14. ognik

    MHB Matrix Sum of Squares: Rotate Coord System to Express as Diagonal

    Maybe I just need help understanding the question ... write $ x^2 + 2xy + 2yz + z^2 $ as a sum of squares $ (x')^2 -2(y')^2 + 2(z')^2 $ in a rotated coord system. The 1st expression $ = \left[ x, y, z \right]M \begin{bmatrix}x\\y\\z\end{bmatrix} $ and I get $ M =...
  15. ognik

    MHB Inertia matrix from orbital angular momentum of the ith element (please check)

    Starting with the orbital angular momentum of the ith element of mass, $ \vec{L}_I = \vec{r}_I \times \vec{p}_I = m_i \vec{r}_i \times \left( \omega \times \vec{r}_i\right) $, derive the inertia matrix such that $\vec{L} =I\omega, |\vec{L} \rangle = I |\vec{\omega} \rangle $ I used a X b X c...
  16. ognik

    MHB Show that the eigenvalues of any matrix are unaltered by a similarity transform

    Show that the eigenvalues of any matrix are unaltered by a similarity transform - the book says this follows from the invariance of the secular equation under a similarity transform - which is news to me. The secular eqtn is found by Det(A-\lambda I)=0 and is a poly in \lambda , so I can't see...
  17. R

    How to Input and Display a Matrix in Matlab?

    Homework Statement I have to make program that a user inputs a matrix and program displays it.Homework EquationsThe Attempt at a Solution I know the logic as in c++ I am able to display that. Here, m=input('Enter rows of matrix'); % Why not double quotes here as in cout of C++? n=input('Enter...
  18. R

    Comp Sci C++ Sum of prime numbers in matrix

    Homework Statement My Program is not showing the sum value or not returning it. A blank space is coming.Why that is so? Homework Equations Showing the attempt below in form of code. The Attempt at a Solution #include<iostream.h> #include<conio.h> Prime_Sum(int arr[30][30],int m, int n); void...
  19. Alfreds9

    Maximum useful matrix size for radiation counting?

    Hi, I'd like to know if there is a maximum matrix size after which radiation counting (using a scintillator/photomultiplier) on a flat paper sample doesn't improve or is not significant. Specifically this would refer to radiochromatograms, or chromatography strips of radioactive samples. If...
  20. ognik

    MHB Uniqueness of Inverse Matrices: Proof and Explanation

    I have an exercise which says to show that for vectors, $ A \cdot A^{-1} = A^{-1} \cdot A = I $ does NOT define $ A^{-1}$ uniquely. But, let's assume there are at least 2 of $ A^{-1} = B, C$ Then $ A \cdot B = I = A \cdot C , \therefore BAB = BAC, \therefore B=C$, therefore $ A^{-1}$ is...
  21. ognik

    MHB Proving the Pauli Matrix Identity with Ordinary Vectors: A Simplified Approach

    I'm not sure I have the right approach here: Using the three 2 X 2 Pauli spin matrices, let $ \vec{\sigma} = \hat{x} \sigma_1 + \hat{y} \sigma_2 +\hat{z} \sigma_3 $ and $\vec{a}, \vec{b}$ are ordinary vectors, Show that $ \left( \vec{\sigma} \cdot \vec{a} \right) \left( \vec{\sigma} \cdot...
  22. D

    Diagonal Scaling of a 2x2 Positive Definite Matrix

    Given a Positive Definite Matrix ## A \in {\mathbb{R}}^{2 \times 2} ## given by: $$ A = \begin{bmatrix} {A}_{11} & {A}_{12} \\ {A}_{12} & {A}_{22} \end{bmatrix} $$ And a Matrix ## B ## Given by: $$ B = \begin{bmatrix} \frac{1}{\sqrt{{A}_{11}}} & 0 \\ 0 & \frac{1}{\sqrt{{A}_{22}}}...
  23. Einj

    What combination of generators can produce a particular SU(2) matrix?

    Hello everyone, I have a question that will probably turn out to be trivial. I have the following matrix: $$ U=\text{diag}(e^{2i\alpha},e^{-i\alpha},e^{-i\alpha}). $$ This seems to me as an SU(2) matrix in the adjoint representation since it's unitary and has determinant 1. Am I right? If so...
  24. W

    Eigenvalues of a 2x2 Matrix: What's the Mistake?

    Homework Statement Find the eigenvalues of the matrix ## \left( \begin{array}{cc} 3 & -1.5\\ -1.5 & -1\\ \end{array} \right) ## It's probably a really stupid mistake, but the answer I get doesn't match the answer from wolfram alpha's eigenvalue calculator... always a bad sign. Homework...
  25. B

    MHB Proving A is Zero Matrix if B is Invertible & Same Size as A

    Show that if A and B are square matrices of the same size such that B is an invertible matrix, then A must be a zero matrix.
  26. kostoglotov

    How can e^{Diag Matrix} not be an infinite series?

    So, in a section on applying Eigenvectors to Differential Equations (what a jump in the learning curve), I've encountered e^{At} \vec{u}(0) = \vec{u}(t) as a solution to certain differential equations, if we are considering the trial substitution y = e^{\lambda t} and solving for constant...
  27. S

    Simple showing inverse of matrix also upper triangular

    I'm trying to show that A be a 3 x 3 upper triangular matrix with non-zero determinant . Show by explicit computation that A^{-1}(inverse of A) is also upper triangular. Simple showing is enough for me. \begin{bmatrix}\color{blue}a & \color{blue}b & \color{blue}c \\0 & \color{blue}d &...
  28. Msilva

    Finding a matrix representation for operator A

    I need to find a matrix representation for operator A=x\frac{d}{dx} using Legendre polinomials as base. I would use a_{mn}=\int^{-1}_{-1}P_m(x)\,x\frac{d}{dx}\,P_n(x)\,dx, but I have the problem that Legendre polinomials aren't orthonormal \langle P_{i}|P_{l}\rangle=\delta_{il}\frac{2}{2i+1}. I...
  29. V

    Can Matrix Determinants Be Used to Find Optimal Area in Higher Dimensions?

    It is possible to find area of triangle or parallelogram in euclidean by using matrix determinant composed of unity, x coeffs and y coeffs in row1,2,3 respectively. Is it possible to do that in higher dimensions as well although it may be not as simple as in 2D case. In 3d matrix composed of...
  30. A

    MHB Solving 2x2 Matrix Projection Problem: Strang's Approach

    Many important techniques in fields such as CT and MR imaging in medicine, nondestructive testing and scientific visualization are based on trying to recover a matrix from its projections. A small version of the problem is given the sums of the rows and columns of a 2 x 2 matrix, determine the...
  31. B

    Showing that the Entries of a Matrix Arise As Inner Products

    Homework Statement Let ##B \in M_n (\mathbb{C})## be such that ##B \ge 0## (i.e., it is a positive semi-definite matrix) and ##b_{ii} = 1## (ones along the diagonal). Show that there exists a collection of ##n## unit vectors ##\{e_1,...,e_n \} \subset \mathbb{C}^n## such that ##b_{ij} = \langle...
  32. kostoglotov

    Matrix with repeated eigenvalues is diagonalizable....?

    MIT OCW 18.06 Intro to Linear Algebra 4th edt Gilbert Strang Ch6.2 - the textbook emphasized that "matrices that have repeated eigenvalues are not diagonalizable". imgur: http://i.imgur.com/Q4pbi33.jpg and imgur: http://i.imgur.com/RSOmS2o.jpg Upon rereading...I do see the possibility...
  33. RJLiberator

    Unitary Matrix preserves the norm Proof

    Homework Statement Let |v> ∈ ℂ^2 and |w> = A|v> where A is an nxn unitary matrix. Show that <v|v> = <w|w>. Homework Equations * = complex conjugate † = hermitian conjugate The Attempt at a Solution Start: <v|v> = <w|w> Use definition of w <v|v>=<A|v>A|v>> Here's the interesting part Using...
  34. W

    Proving the Existence of a Rotation Matrix from Given Relations

    Homework Statement Let A∈M2x2(ℝ) such that ATA = I and det(A) = -1. Prove that for ANY such matrix there exists an angle θ such that A = ## \left( \begin{array}{cc} cos(\theta) & sin(\theta)\\ sin(\theta) & -cos(\theta)\\ \end{array} \right) ## It is not sufficient to show that this matrix...
  35. M

    Observable System L Matrix, can a value be negative?

    Homework Statement An error matrix is in the form, has a characteristic equation: ## CE: s^2 + 120s + 7200 = 0 ## A state variable feedback system is described by: ## A_F = \begin{bmatrix}0 & 1 \\-616.8 & -40 \end{bmatrix} ## ## B = \begin{bmatrix}0 \\ 1 \end{bmatrix} ## ## C =...
  36. MathematicalPhysicist

    Exploring Conjectures in a Random Matrix Model - arXiv Study

    Is any of the conjectures in: http://arxiv.org/pdf/hep-th/9610043v3.pdf have been proven/disproven? what has been left still open? I am thinking of reading this article sometime in the future, hope it's digestable (but first need to finish my studies of QFT and GR.)
  37. F

    How Do You Calculate Expectation Values in Quantum Mechanics?

    Homework Statement A system's state of spin 1/2 is represented at t=0 by C*exp[-a2(p-p0)2]*{{1,0},{0,1}} where the density matrix is represented in the base of eighenvalues of Sz and the spatial vector is represented in the continuum base of statesPx, Py, Pz. Find <X>, <Px> and <ΔX>, <ΔPx>...
  38. evinda

    MATLAB Troubleshooting a MATLAB Error: Inner Matrix Dimensions Must Agree

    Hello! (Wave) I have written the following code in matlab: function v=uexact(x,t) v=sin(2*pi*x)*exp(-4*pi^2*t); end function [ex]=test3 h = 1/50; T=1/2500; x=0:h:1; t=0:T:1; ex=uexact(x,t); end I...
  39. S

    Fundamental matrix vs Wronskian

    I have just learned the first order system of ODE, i found that the Wronskian in second order ODE is |y1 y2 ; y1' y2'| but in first order system of ODE is the Wronskian is W(two solution), i wonder which ones is the general form? thank you very much
  40. davidbenari

    Matrix method to find coefficients of 1-d S.E.

    I haven't taken a course on quantum mechanics yet, but I was asked to solve (numerically) ##[-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+V(x)]\phi(x)=E\phi(x) ## ##V(x)=2000(x-0.5)^2## by supposing the solution is ##\sum_{0}^{\infty} a_n \phi_n(x)## and ##\phi_n(x)## is the typical solution to the a...
  41. R

    Eigenvector of Pauli Matrix (z-component of Pauli matrix)

    I have had no problem while finding the eigen vectors for the x and y components of pauli matrix. However, while solving for the z- component, I got stuck. The eigen values are 1 and -1. While solving for the eigen vector corresponding to the eigen value 1 using (\sigma _z-\lambda I)X=0, I got...
  42. S

    How to Solve the Exponential of a Matrix?

    Please help me understand the following step
  43. A

    Can a Matrix A² ever equal -I₃ in M₃(ℝ)?

    Homework Statement Show that no matrix A ∈ M3 (ℝ) exists so that A2 = -I3 Homework EquationsThe Attempt at a Solution This is from a french textbook of first year linear algebra. I'm quite familiar with properties of matrices but I don't have any idea of how to prove this. Thanks for the help!
  44. PsychonautQQ

    Finding a matrix to represent a 2x2 transpose mapping

    Homework Statement Let L be a mapping such that L(A) = A^t, the transpose mapping. Find a matrix representing L with respect to the standard basis [1,1,1,1] Homework EquationsThe Attempt at a Solution So should I end up getting a 4x4 matrix here? I got 1,0,0,0 for the first column, 0,0,1,0 for...
  45. G

    How Do You Calculate the System Matrix for a Lens After a Beam Waist?

    Homework Statement A thin lens is placed 2m after the beam waist. The lens has f = 200mm. Find the appropriate system matrix. This is a past exam question I want to check I got right. Homework Equations For some straight section [[1 , d],[0 , 1]] and for a thin lens [[1 , 0],[-1/f , 1]]...
  46. K

    Is the moment of inertia matrix a tensor?

    Homework Statement Is the moment of inertia matrix a tensor? Hint: the dyadic product of two vectors transforms according to the rule for second order tensors. I is the inertia matrix L is the angular momentum \omega is the angular velocity Homework Equations The transformation rule for a...
  47. Daaavde

    Covariance matrix with asymmetric uncertainties

    Hello everyone, I'm currently building the covariance matrix of a large dataset in order to calculate the Chi-Squared. The covariance matrix has this form: \begin{bmatrix} \sigma^2_{1, stat} + \sigma^2_{1, syst} & \rho_{12} \sigma_{1,syst} \sigma_{2, syst} & ... \\ \rho_{12} \sigma_{1,syst}...
  48. Calpalned

    Rewriting Third Column: Wronskian Matrix Homework Guide

    Homework Statement Page 133 Homework Equations n/a The Attempt at a Solution What is the process for rewriting the third column? 2x-3 and be rewritten as 2x, and 2-3cosx can be rewritten as 2. I don't get this.
  49. M

    Can the basis minor of a matrix be the matrix itself?

    Hello I am trying to learn linear algebra, and I came across this definition of basis minor on this webpage: https://en.wikibooks.org/wiki/Linear_Algebra/Linear_Dependence_of_Columns "The rank of a matrix is the maximum order of a minor that does not equal 0. The minor of a matrix with the...
  50. D

    Demonstrate the matrix represents a 2nd order tensor

    Homework Statement Demonstrate that matrix ##T## represents a 2nd order tensor ##T = \pmatrix{ x_2^2 && -x_1x_2 \\ -x_1x_2 && x_1^2}## Homework Equations To show that something is a tensor, it must transform by ##T_{ij}' = L_{il}L_{jm}T_{lm}##. I cannot find a neat general form for ##T_{ij}##...
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