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. O

    Strange results with transfer matrix (Optics)

    Hi everyone, I'm trying to study reflection on the rear side of an optical device. I wrote a transfer-matrix code in MATLAB to compute the reflectance. I checked my code by comparing some basic cases with other kind of optical simulations (FTDT with Lumerical). When the incident medium is Air...
  2. G

    Compliance matrix from strain matrix, Matlab

    Homework Statement (I'm trying to replicate some results in an academic paper where they have calculated elastic properties of a crystal. Because I'm going to do a lot of similar time-consuming calculations following this one, I need to learn how to do them using a computer.) The compliance...
  3. Math Amateur

    MHB Triangular Matrix RIngs .... Lam, Proposition 1.17

    I am reading T. Y. Lam's book, "A First Course in Noncommutative Rings" (Second Edition) and am currently focussed on Section 1:Basic Terminology and Examples ... I need help with Part (1) of Proposition 1.17 ... ... Proposition 1.17 (together with related material from Example 1.14 reads...
  4. Math Amateur

    I Triangular Matrix RIngs .... Lam, Proposition 1.17

    I am reading T. Y. Lam's book, "A First Course in Noncommutative Rings" (Second Edition) and am currently focussed on Section 1:Basic Terminology and Examples ... I need help with Part (1) of Proposition 1.17 ... ... Proposition 1.17 (together with related material from Example 1.14 reads as...
  5. Math Amateur

    MHB Triangular Matrix Rings .... Another Question

    I am reading T. Y. Lam's book, "A First Course in Noncommutative Rings" (Second Edition) and am currently focussed on Section 1:Basic Terminology and Examples ... I need help with yet another aspect of Example 1.14 ... ... Example 1.14 reads as follows: Near the end of the above text from...
  6. Math Amateur

    I Triangular Matrix RIngs .... Another Question

    I am reading T. Y. Lam's book, "A First Course in Noncommutative Rings" (Second Edition) and am currently focussed on Section 1:Basic Terminology and Examples ... I need help with yet another aspect of Example 1.14 ... ... Example 1.14 reads as follows: Near the end of the above text from T...
  7. A

    Extract Matrix Elements in Circular Manner

    Lets say I have a matrix A=rand(31,51). How can I extract its elements from its center (say row = 15, column = 26) in circular manner. I want to have a matrix that displays only those elements of 'A' which are inside a circle with its center at A(15,26). Radius of circle can be any number say 5...
  8. grassstrip1

    Vandermonde Determinant for NxN Matrices

    The problem I have is this: Show that \begin{bmatrix} 1 & 1 & 1 \\ λ_{1} & λ_{2} & λ_{3} \\ λ_{1}^{2} & λ_{2}^{2} & λ_{3}^{2} \end{bmatrix} Has determinant $$ (λ_{3} - λ_{2}) (λ_{3} - λ_{1}) (λ_{2} - λ_{1}) $$ And generalize to the NxN case (proof not needed)Obviously solving the 3x3 was...
  9. S

    Determinant of a 3x3 matrix via row reduction

    Homework Statement Show that the determinant of is (a-b)(b-c)(c-a) Homework Equations Row reduction, determinants The Attempt at a Solution Apparently I got a (a-b)^2 instead of (a-b) when I multiplied them up. It would be grateful if someone can point me out where the mistakes are.
  10. A

    I Why do eigenvectors stay the same when a matrix is squared?

    I am new to linear algebra but I have been trying to figure out this question. Everybody seems to take for granted that for matrix A which has eigenvectors x, A2 also has the same eigenvectors? I know that people are just operating on the equation Ax=λx, saying that A2x=A(Ax)=A(λx) and...
  11. L

    A Maurer–Cartan forms for a matrix group?

    I am very confused about that in some literature the Maurer Cartan forms for a matrix group is written as ##{\omega _g} = {g^{ - 1}}dg## what is ##dg## here? can anyone give an example explicitly? My best guess is ## dg = \left( {\begin{array}{*{20}{c}} {d{x^{11}}}& \ldots &{d{x^{1m}}}\\...
  12. TheSodesa

    Proving two simple matrix product properties

    Homework Statement Let ##A## be an n × p matrix and ##B## be an p × m matrix with the following column vector representation, B = \begin{bmatrix} b_1 , & b_2, & ... & ,b_m \end{bmatrix} Prove that AB = \begin{bmatrix} Ab_1 , & Ab_2, & ... & , Ab_m \end{bmatrix} If ##A## is represented...
  13. arpon

    I Are the columns space and row space same for idempotent matrix?

    Suppose, ##A## is an idempotent matrix, i.e, ##A^2=A##. For idempotent matrix, the eigenvalues are ##1## and ##0##. Here, the eigenspace corresponding to eigenvalue ##1## is the column space, and the eigenspace corresponding to eigenvalue ##0## is the null space. But eigenspaces for distinct...
  14. J

    I What's the geometric interpretation of the trace of a matrix

    Hello, I was just wondering if there is a geometric interpretation of the trace in the same way that the determinant is the volume of the vectors that make up a parallelepiped. Thanks!
  15. M

    How to Find Ψ(x,t) for a Given Hamiltonian Matrix and Initial State?

    Homework Statement I have the matrix form of the Hamiltonian: H = ( 1 2-i 2+i 3) If in the t=0, system is in the state a = (1 0)T, what is Ψ(x,t)? Homework Equations Eigenvalue equation The Attempt at a Solution So, I have diagonalized given matrix and got...
  16. L

    Finding Eigenvalues and Wave Function in a Basis of Orthonormalized Vectors

    Homework Statement Eigenvalues of the Hamiltonian with corresponding energies are: Iv1>=(I1>+I2>+I3>)/31/2 E1=α + 2β Iv2>=(I1>-I3>) /21/2 E2=α-β Iv3>= (2I2> - I1> I3>)/61/2 E3=α-β Write the matrix of the Hamiltonian in the basis of...
  17. M

    Proving a matrix is orthogonal

    Homework Statement Show that the matrix ##P = \big{[} p_{ij} \big{]}## is orthogonal. Homework Equations ##P \vec{v} = \vec{v}'## where each vector is in ##\mathbb{R}^3## and ##P## is a ##3 \times 3## matrix. SO I guess ##P## is a transformation matrix taking ##\vec{v}## to ##\vec{v}'##. I...
  18. A

    Matrix representation of certain Operator

    Homework Statement Vectors I1> and I2> create the orthonormal basis. Operator O is: O=a(I1><1I-I2><2I+iI1><2I-iI2><1I), where a is a real number. Find the matrix representation of the operator in the basis I1>,I2>. Find eigenvalues and eigenvectors of the operator. Check if the eigenvectors are...
  19. M

    Matrix Operations: Inverse Existence & Row Op.

    Homework Statement [/B] \begin{array}{cc}1 & 1&1\\ 1&1-s&1-s\\-s&1-s&s^2-1\end{array} a)For which values of s does the inverse exist, and why? You should be using row operations and ideally head for reduced row echelon form b) In the process of calculating part a), you will come across a...
  20. munirah

    From density matrix, how can I know what state it belongs to

    Homework Statement Given a density matrix of three qubit pure state, how can I know after do some transformation, this state belong to what class?. Class I mean here, either separable state, biseparable, GHZ state or W state? I mean here what is the indicator to me classify it? It is the...
  21. Ken Gallock

    I What is the name of the matrix decomposition with specific properties?

    Hi everyone. There is the ##2\times 2## matrix ##B## $$B= \left[ \begin{array}{cc} B_{11} &B_{12} \\ B_{21}&B_{22} \end{array} \right],~B_{ij}\in \mathbb{C} $$ with property $$\vert B_{11}\vert^2 + \vert B_{12}\vert^2=1,$$ $$\vert B_{21}\vert^2 + \vert B_{22}\vert^2=1,$$...
  22. Sophrosyne

    I How Does Heisenberg's Matrix Mechanics Relate to Dirac's Notation?

    I have been trying to read about Heisenberg's matrix mechanics on my own, and I am getting hopelessly lost. I understand it has something to do with anharmonic oscillators. I am no physicist, so please take it easy with the explanations. Also, I read somewhere that these, along with Max...
  23. A

    B Is the Inverse of this Matrix Possible?

    I tried to find the inverse of below matrix and what I get is no inverse. ## \left( \begin{array}{rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} \right) ## Can someone please check it whether I am correct or not?
  24. J

    Matrix riccati differential equation using matlab

    Homework Statement Homework EquationsThe Attempt at a Solution
  25. S

    A Rank 3x4 Complex Matrix Constraints

    I am dealing with a 3x4 complex matrix M that relates a vector d to another vetor c. That is: c = [M]*d d is 4x1 and c is 3x1. I want to introduce a new line (constraint) into M, say d(1) = d(2). However, I would like to only apply the constraint to the real or only the imaginary parts. Is...
  26. Mohamed_Wael

    Stiffness Matrix of Frictionless Plate Support: Puzzling Differences

    Hi all, In the attached photo, you can find a plate supported along the edge by "frictionless" support and I am trying to obtain the stiffness matrix using the node at the center. I wonder why the Kxx and Kyy (highlighted) are not equivalent or even near to each other, any suggestions?
  27. Mohamed_Wael

    How can I determine the overall stiffness matrix for a structure using Ansys?

    Hi, I know that Ansys APDL can determine the stiffness matrix for any structure, I would like to know if I can determine the overall stiffness for this structure or not if yes how can I do this? thanks.
  28. Z

    I Solving equations with singular matrix

    Hi! I have a problem: I need to solve an equation, Ax=y, where A is a known matrix, y is a known column vector and x is an unknown column vector. Unfortunately, A is singular so I cannot do the simple solution of inverse(A)*y=x. Does anybody know of any way that I can obtain the coefficients...
  29. Larry Gopnik

    LaTeX Placing greyscale .jpg images into a matrix

    Hi, I hope someone can help me! I could not find a solution online of which could help me. My problem: I have imagecubes - they are a "cube" of 10 images of the same place of a photo, one at 400nm, one at 450nm etc etc. I need to upload these into MATLAB so I can then analyse the intensities...
  30. L

    Density matrix spin half, Pauli vector

    A nice discussion of the density operator for a qubit can be found here: http://www.vcpc.univie.ac.at/~ian/hotlist/qc/talks/bloch-sphere-rotations.pdf
  31. S

    MHB How can I find out if this matrix A's columns are linearly independent?

    How can I find out if this matrix A's columns are linearly independent? $\begin{bmatrix}1&0\\0&0\end{bmatrix}$ I see here that $x_1 = 0$ and similarly $x_2 = 0$ does this mean that this matrix A's columns are therefore linearly dependent? Also this is a projection onto the $x_1$ axis so is it...
  32. L

    Can buffing affect the readability of engraved data matrix on steel?

    The company I work for makes and repairs circular saw blades. When we receive blades in from companies, they must be checked into our system manually using an ID number, and we are looking for a way to check them in by scanning, like a data matrix. We have sent out several blades to companies...
  33. J

    Can You Solve for the Positive Definite Matrix with Eigenvalues 1 and 2?

    Homework Statement a positive definite matrix has eigenvalues λ=1 and λ=2. find the matrix Homework EquationsThe Attempt at a Solution I've used a 2x2 matrix with entries a0,a1,a2,a3 as the unknown matrix but no use. (As little as i know a0 and a3 should be 1 and 2 respectively...
  34. S

    I Matrix of columns of polynomials coefficients invertibility

    I am reviewing the method of partial fraction decomposition, and I get to the point that I have a matrix equation that relates the coefficients of the the original numerator to the coefficients of the numerators of the partial fractions, with the each column corresponding to a certain polynomial...
  35. D

    Partial fraction decomposition using matrix

    Homework Statement Hello! I am doing a chapter on partial fraction decomposition, and it seems I do not understand it correctly. Here is the exercise doing which I get wrong answers. Please, take a look at the way I proceed and, please, let me know what is wrong in my understanding. Homework...
  36. M

    Linear Algebra: 2x2 matrix raised to the power of n

    Homework Statement If n is a positive integer, then 2x2 matrix [-32,252] [-4,32] raised to the power of n is... Homework Equations I know that first I should diagonalize the given matrix, something I also seem to have a hard time with. The Attempt at a Solution I determined the eigenvalues...
  37. M

    Linear Algebra: Matrix Transformation

    Homework Statement Find the matrix that represents a rotation counterclockwise around the origin by 75 degrees followed by a reflection about the x-axis Homework Equations I know that for A rotated counter clockwise you use the 2x2 matirx [cos(theta), -sin(theta)] [sin(theta, cos(theta)] and...
  38. mertcan

    I Jacobian matrix generalization in coordinate transformation

    hi, I always see that jacobian matrix is derived for just 2 dimension ( ıt means 2x2 jacobian matrix) in books while ensuring the coordinate transformation. After that kind of derivation, books say that you can use same principle for higher dimensions. But, I really wonder if there is a proof...
  39. Xico Sim

    I Transition matrix element and Isospin

    Hi, guys. A type of problem that often appears is to find the relation between cross sections of some processes. An example would be: $$\pi _{- }+ p \rightarrow K_0 + \Sigma_0$$ $$\pi _{- }+ p \rightarrow K_+ + \Sigma_-$$ $$\pi _{+}+ p \rightarrow K_+ + \Sigma_+$$ To do this, I argue that...
  40. D

    Diagonalizability of Singular Matrices: Investigating Rank and Eigenvectors

    Homework Statement Let A be a 3x3 singular Matrix that satisfy: p(A+5I) < p(A) p - is the rank of the matrix I - is the identity matrix, Is A Diagonalizable? Homework EquationsThe Attempt at a Solution I know that A diagonalizable matrix can be Singular from every rank, even at 0 rank, so i...
  41. D

    Find inverse matrix using determinants and adjoints

    Hello! Please, help me to see my mistake - for quite a while I can't solve a very easy matrix. I have to find the inverse of the given matrix using their determinants and adjoints. 4 6 -3 3 4 -3 1 2 6 to find adjoint matrix I need to find cofactors 11, 12, etc till 33. Cofactor11 =...
  42. kelvin490

    MATLAB How can I append new columns to an existing Excel file with MATLAB?

    I would like to ask how to use MATLAB to append new columns into existing excel file without altering the original data in the file? In my case I don't know the original number of columns and rows in the file and it is inefficient to open the files one by one and check in practice. Another...
  43. munirah

    I How reduced density matrix obtained from the matrix.

    Can any expert help me in explaining how this example below get the reduced density matrix from the density matrix in bipartite system. $$\rho =\frac{1}{4}\begin{pmatrix} 1 & 1 & cos(\frac{\alpha}{2})-sin(\frac{\alpha}{2}) & cos(\frac{\alpha}{2})+sin(\frac{\alpha}{2}) \\ 1 & 1 &...
  44. munirah

    Reduced Density operator in matrix form

    Homework Statement I already read book of Quantum Computation and Quantum Information by Nielsen and Chuang according to reduced density operator and I already understand how to do the reduced density using Dirac notation, Ket Bra.Homework Equations [/B] My problem here I want to know the...
  45. P

    MHB Sava's question via email about matrix multiplication

    $\displaystyle \begin{align*} A\,A^T &= \left[\begin{matrix} 3 & 0 & -4 \\ 4 & 0 & \phantom{-}3 \\ 0 & 5 & \phantom{-}0 \end{matrix}\right]\left[ \begin{matrix} \phantom{-}3 & 4 & 0 \\ \phantom{-}0 & 0 & 5 \\ -4 & 3 & 0 \end{matrix}\right] \\ &= \left[ \begin{matrix} 3\cdot 3 + 0 \cdot 0 +...
  46. B

    Prove 3x3 Skew symmetric matrix determinant is equal to zero

    Homework Statement Hi there, I'm happy with the proof that any odd ordered matrix's determinant is equal to zero. However, I am failing to see how it can be done specifically for a 3x3 matrix using only row and column interchanging. Homework Equations I have attached the determinant as an...
  47. tommyxu3

    I Proving Identity for Determinant of $A^tA$

    I have a problem of proving an identity about determinants. For ##A\in M_{m\times n}(\mathbb{R}),## a matrix with ##m## rows and ##n## columns, prove the following identity. $$|\det(A^tA)|=\sum_{1\le j_1\le ... \le j_n \le m} (det(A_{j_1...j_n}))^2$$ where ##A_{j_1...j_n}## is the matrix whose...
  48. J

    MCNP multigroup scattering matrix and diffusion coefficient

    Hello I am a lower-intermediate user of MCNP and I do not know how to obtain the diffusion coefficient (or maybe the angle of scattering) using tallies. I also have read a paper (Multigroup Scattering Matrix Generation Method using Weight-to-Flux Ratio Based on a Continous Energy Monte Carlo...
  49. U

    I Spherical coordinates via a rotation matrix

    First, I'd like to say I apologize if my formatting is off! I am trying to figure out how to do all of this on here, so please bear with me! So I was watching this video on spherical coordinates via a rotation matrix: and in the end, he gets: x = \rho * sin(\theta) * sin(\phi) y = \rho*...
  50. H

    Finding a matrix representation of a Hamiltonian.

    Homework Statement The Hamiltonian H for a certain physical quantum mechanical system has three eigenvectors {|v1>, |v2>, |v3>} satisfying: H|vj> = (2-j)a|vj> Write down the matrix representing H in the representation {|v1>, |v2>, |v3>} . Homework EquationsThe Attempt at a Solution I though...
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