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.

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  1. 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...
  2. 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...
  3. 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...
  4. 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}...
  5. 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...
  6. 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...
  7. 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...
  8. 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...
  9. 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...
  10. 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"...
  11. 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...
  12. 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
  13. 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?
  14. 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'...
  15. 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##...
  16. 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...
  17. 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.
  18. 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...
  19. B

    MHB Solve System Using Matrix Inverse

  20. 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...
  21. 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...
  22. 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:
  23. N

    I How was this dynamical matrix solved?

    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!
  24. 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) {...
  25. 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)...
  26. 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...
  27. 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...
  28. 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...
  29. 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...
  30. 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
  31. 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...
  32. Haorong Wu

    I Improper density matrix with negative eigenvalues

    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...
  33. Haorong Wu

    The representation matrix for alpha and beta in Dirac equation

    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...
  34. E

    Why is this matrix not working in my program?

    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...
  35. S

    Diagonalizing a matrix given the eigenvalues

    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...
  36. M

    MHB F convex iff Hessian matrix positive semidefinite

    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...
  37. N

    A Trace of the inverse of matrix products

    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...
  38. S

    Linear Algebra uniqueness of solution

    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...
  39. PainterGuy

    LaTeX How do I fix this generated LaTex code for a matrix?

    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...
  40. Z

    B Which one is correct? (the Matrix or Wave formulation of QM)

    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 ?
  41. I

    Comp Sci Matrix problem in java using bubble sort

    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...
  42. W

    MHB Find Eigenvalues & Basis C2 Matrix: Help!

    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!
  43. W

    MHB Solving Matrix A: Characteristic Equation and Eigenvectors

    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...
  44. waynewec

    I Reducing NxN Matrix to 2x2 w/ Physical Constraints

    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} =...
  45. A

    A Question about a property of a matrix of transition probabilities

    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##)...
  46. D

    I Normalization of an Eigenvector in a Matrix

  47. F

    I Change of Basis Matrix vs Transformation matrix in the same basis....

    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...
  48. R

    Prove that If A,B are 3x3 tensors, then the matrix C=AB is also a tensor

    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 (:
  49. PainterGuy

    Proving the results for the trace of a matrix

    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...
  50. LCSphysicist

    Matrix in momentum representation

    $$\langle p | W | p' \rangle = \int \langle p | x \rangle \langle x W | x' \rangle \langle x' p' \rangle dx dx'$$ $$\langle p | W | p' \rangle = \int \langle p | x \rangle \delta(x-x') W(x) \langle x' | p' \rangle dx dx'$$ $$\langle p | W | p' \rangle = \int \langle p | x' \rangle W(x') \langle...
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