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. 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...
  2. 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...
  3. 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...
  4. 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...
  5. 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...
  6. 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 $$\vert B_{11}\vert^2 + \vert B_{12}\vert^2=1,$$ $$\vert B_{21}\vert^2 + \vert B_{22}\vert^2=1,$$...
  7. 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...
  8. 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?
  9. J

    Matrix riccati differential equation using matlab

    Homework Statement Homework EquationsThe Attempt at a Solution
  10. 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...
  11. 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?
  12. 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.
  13. 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...
  14. 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...
  15. 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
  16. 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...
  17. 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...
  18. 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...
  19. 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...
  20. 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...
  21. 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...
  22. 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...
  23. 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...
  24. 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...
  25. 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...
  26. 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 =...
  27. 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...
  28. 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 &...
  29. 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...
  30. 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 +...
  31. 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...
  32. 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...
  33. 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...
  34. 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*...
  35. 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...
  36. F

    Perturbation matrix: free electron model on a square lattice

    Homework Statement Nearly free electron model in a 2D lattice. Consider a divalent 2D metal with a square lattice and one atom per primitive lattice cell. The periodic potential has two Fourier components V10 and V11, corresponding to G = (1,0) and (1,1). Both are negative and mod(V10) >...
  37. B

    MHB Total Labor Cost Per Good Matrix Calculation

    This is probably a simple question A factory produce a good that requires 3 labor-hours in the assembly department and 1 labor-hour in the finishing department. Assembly personnel receive 19 per hour and finishing personnel receive 16 per hour. I need to write a matrix or vector product that...
  38. P

    Finding a matrix for a linear transformation

    'Homework Statement Find the matrix A' for T: R2-->R2, where T(x1, x2) = (2x1 - 2x2, -x1 + 3x2), relative to the basis B' {(1, 0), (1, 1)}. Homework Equations B' = {(1, 0), (1, 0)} so B'-1 = {(1, -1), (0, 1)}. The Attempt at a Solution I'm confused at what exactly a transform matrix...
  39. D

    A Interpretation of the EM tensor as a rotation matrix

    In special relativity, the electromagnetic field is represented by the tensor $$F^{\mu\nu} = \begin{pmatrix}0 & -E_{x} & -E_{y} & -E_{z}\\ E_{x} & 0 & -B_{z} & B_{y}\\ E_{y} & B_{z} & 0 & -B_{x}\\ E_{z} & -B_{y} & B_{x} & 0 \end{pmatrix}$$ which is an anti-symmetric matrix. Recalling the...
  40. D

    I What is the derivative of a matrix transpose?

    Hi! As the title says, what is the derivative of a matrix transpose? I am attempting to take the derivative of \dot{q} and \dot{p} with respect to p and q (on each one). Any advice?
  41. entropy1

    I Expectation value in terms of density matrix

    It says in Susskind's TM: ##\langle L \rangle = Tr \; \rho L = \sum_{a,a'}L_{a',a} \rho_{a,a'}## with ##a## the index of a basisvector, ##L## an observable and ##\rho## a density matrix. Is this correct? What about the trace in the third part of this equation?
  42. P

    Linear transformation representation with a matrix

    Homework Statement For the linear transformation T: R2-->R2 defined by T(x1, X2) = (x1 + x2, 2x1 - x2), use the matrix A to find T(v), where v = (2, 1). B = {(1, 2), (-1, 1)} and B' = {(1, 0), (0, 1)}.Homework Equations T(v) is given, (x1+x2, 2x1-x2) The Attempt at a Solution Okay, I see...
  43. odietrich

    I General form of symmetric 3x3 matrix with only 2 eigenvalues

    I'm looking for the general form of a symmetric 3×3 matrix (or tensor) ##\textbf{A}## with only two different eigenvalues, i.e. of a matrix with the diagonalized form ##\textbf{D}=\begin{pmatrix}a& 0 & 0\\0 & b & 0\\0 & 0 & b\end{pmatrix} = \text{diag}(a,b,b)##. In general, such a matrix can be...
  44. S

    Matrix representation of function composition

    Am I on the right path here? 1. Homework Statement i. Prove that ##T_{a}## and ##T_{b}## are linear transformations. ii. Compose the two linear transformations and show the matrix that represents that composition. 2. The attempt at a solution i. Prove that ##T_{a}## and ##T_{b}## are linear...
  45. J

    I Multiplication by a matrix in GL rotates a plane's basis?

    Let A = (a_{ij}) be a k\times n matrix of rank k . The k row vectors, a_i are linearly independent and span a k-dimensional plane in \mathbb{R}^n . In "Geometry, Topology, and Physics" (Ex 5.5 about the Grassmann manifold), the author states that for a matrix g\in...
  46. L

    Statistical physics. Density matrix

    Homework Statement A system is subject to Hamiltonian ##\hat{H}=-\gamma B_z \hat{S}_z##. Write down the density matrix.[/B]Homework Equations For canonical ensemble ##\hat{\rho}=\frac{1}{Tr(e^{-\beta \hat{H}})}e^{-\beta \hat{H}}## In general ##\rho=\sum_m |\psi_m\rangle \langle \psi_m|## The...
  47. V

    Mesh current equation in matrix form

    i3 -? This is how I tried to solve using cramer's rule (denominator is the determinant of the matrix, while numerator is the determinant of the modified matrix) I ignored the prefix Kilo, but the method is right. So I get a different value for i3. Does anyone know what's wrong?
  48. KT KIM

    I Matrix Representation of Linear Transformation

    This is where I am stuck. I studied ordered basis and coordinates vector previous to this. of course I studied vector space, basis, linear... etc too, However I can't understand just this part. (maybe this whole part) Especially this one which says [[T(b1)]]c...[[T(bn)]]c be a columns of...
  49. rolotomassi

    C/C++ C++ matrix boundary condition problems

    I have created a matrix with a class called Lattice. The lattice is filled with objects of type 'Dipole' which is created with another class. The problem I am having is with boundary conditions when I look for a neighbour. e.g If i pick a dipole on the top row, I want its 'above' neighbour to be...
  50. S

    Finding tensor components via matrix manipulations

    Homework Statement Imagine we have a tensor ##X^{\mu\nu}## and a vector ##V^{\mu}##, with components ## X^{\mu\nu}=\left( \begin{array}{cccc} 2 & 0 & 1 & -1 \\ -1 & 0 & 3 & 2 \\ -1 & 1 & 0 & 0 \\ -2 & 1 & 1 & -2 \end{array} \right), \qquad V^{\mu} = (-1,2,0,-2). ## Find the components of...
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