What is Matrix: Definition and 1000 Discussions

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. 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...
  2. 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 =...
  3. 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...
  4. 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...
  5. 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...
  6. 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...
  7. 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...
  8. 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...
  9. 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...
  10. 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}}}...
  11. 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...
  12. 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...
  13. 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.
  14. 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...
  15. 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 &...
  16. 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...
  17. 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...
  18. 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...
  19. 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...
  20. 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...
  21. 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...
  22. 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...
  23. 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 =...
  24. 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.)
  25. 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>...
  26. 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...
  27. 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
  28. 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...
  29. 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...
  30. S

    Solving Exponential of a Matrix

    Please help me understand the following step
  31. 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!
  32. 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...
  33. 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]]...
  34. 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...
  35. 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}...
  36. 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.
  37. 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...
  38. 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}##...
  39. J

    What is the Most Efficient Method for Finding the Determinant of an nxn Matrix?

    Homework Statement Shown In the picture. I went to the prof for help he said and i quote :" don't use laplas expansion to find the determinate, it will take you for ever." Homework Equations I don't even know how to do this. prof had no notes on this and Boas is a god awful book for learning...
  40. P

    3x3 matrix inverse unit vector

    Homework Statement Hi! I have the 3x3 matrix for L below, which I calculated. But now I need to figure out how the equation below actually means! Is it just the inverse of L (L^-1)? I cannot proceed if I don't know this step. Homework Equations See image The Attempt at a Solution I put in...
  41. evinda

    MHB Calculating Determinant of $(N+1) \times (N+1)$ Matrix

    Hello! (Wave) Suppose that we are given this $(N+1) \times (N+1)$ matrix: $\begin{bmatrix} -(1+h+\frac{h^2}{2}q(x_0)) & 1 & 0 & 0 & \dots & \dots & 0 \\ -1 & 2+h^2q(x_1) & -1 & 0 & \dots& \dots & 0\\ 0 & -1 & 2+h^2q(x_2) & -1 & 0 & \dots & 0\\ & & & & & & \\ & & & & & & \\ & & & & & & \\...
  42. P

    Difference equation and diagonal block matrix

    Homework Statement Compute ##A^j~\text{for} ~~j=1,2,...,n## for the block diagonal matrix##A=\begin{bmatrix} J_2(1)& \\ &J_3(0) \end{bmatrix}##, And show that the difference equation ##x_{j+1}=Ax_{j}## has a solution satisfying ##|x_{j}|\rightarrow\infty~\text{as}~j\rightarrow\infty##...
  43. S

    MHB Matrix Algebra 2.0 Help: Solving Questions with Cosine Laws

    Hey guys, So I'm stuck on another question from the previous one that I posted and would absolutely love it if I can get some help regarding how to attempt this. I literally have no clue at how to go by solving it. I have a feeling for question one that the cosine laws might come in handy but...
  44. L

    Prove that a zero-one matrix can only have 1's after 5th power

    Hello, I couldn't give the full explanation in the title - I am talking about a particular matrix. Given the matrix: A[1] = 0 0 1 1 0 0 1 1 0 A[5] = 1 1 1 1 1 1 1 1 1 Once it gets to the 5th boolean power, it becomes all 1's, and any power greater than or equal to 5 will always produce a...
  45. B3NR4Y

    Comp Sci Store values in an arbitrarily sized matrix C++

    Homework Statement "Calculate the max, min, count, average, and standard deviation (std dev) of a set of numbers. The formula for average is: average is sum divided by count The formula for standard deviation is stddev is the square root of the variance The formula for variance is variance is...
  46. askhetan

    Matrix Elements as images of basis vectors

    I'm trying to understand the maths of QM from Shankar's book - Principles of Quantum Mechanics: On page 21 of that book, there is a general derivation that if we have a relation: |v'> = Ω|v> Where Ω is a operator on |v> transfroming it into |v'>, then the matrix entries of the operator can be...
  47. D

    Find eigenvalues and eigenvectors of weird matrix

    Homework Statement find eigenvalues and eigenvectors for the following matrix |a 1 0| |1 a 1| |0 1 a| Homework EquationsThe Attempt at a Solution I'm trying to find eigenvalues, in doing so I've come to a dead end at 1 + (a^3 - lambda a^2 -2a^2 lambda + 2a lambda^2 + lambda^2 a - lambda^3 - a...
  48. brotherbobby

    Proving "Rotation Matrix is Orthogonal: Necessary & Sufficient

    I'd like to prove the fact that - since a rotation of axes is a length-preserving transformation, the rotation matrix must be orthogonal. By the way, the converse of the statement is true also. Meaning, if a transformation is orthogonal, it must be length preserving, and I have been able to...
  49. kostoglotov

    Matrix is Invertible: is this notation ok?

    Quick question, not even sure if I should post it here, but I can't think where else. If I wanted to write the short hand of A is an invertible matrix, would it be ok to just write A \ \exists A^{-1} ?
  50. ognik

    MHB Help with Matrix & Operator specifics

    Hi, those who have seen my recent posts will know that I am trying to put together a simple table that I am certain will help me get through a cloud of uncertainty that is proving a major obstacle to my on-going studies. I refer to...
Back
Top