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. P

    I Finding the matrix inverse by diagonalisation

    How would you go about doing this, I see it so often quoted as a method, but no-where can I find an example This is what I was thinking D=P^(-1)AP Would it then follow that D^(-1)=P^(-1)A^(-1)P ? My reasoning being: DD^(-1)= P^(-1)APP^(-1)A^(-1)P identity matrix= P^(-1)AA^(-1)P=identity...
  2. Y

    Linear Algebra - Find Orthogonal Matrix Q that diagonals

    Homework Statement I'm told to find the matrix Q of the matrix A Homework EquationsThe Attempt at a Solution So my problem is that in the answer key they have S = (1/3)... and I have no idea where this 1/3 comes from. I get an equivalent answer for X_1, X_2, and X_3 S = [X_1, X_2, X_3] but...
  3. D

    Calculating the frequency response of filter with a matrix

    Homework Statement This is actually part 3 of the question. Part one was to form 7 equations to form a 7x7 matrix, part 2 was to solve it, which I've done. This question is to be done with Matlab, by the way. Part 3: Homework Equations Frequency response = Vout / Vin. The Attempt at a...
  4. siimplyabi

    Matrix Relative to B and B' R3 to R3

    Homework Statement For problems 1 and 2 use http://T: R^3 to R^3, T(<x1,x2,x3>) = <2x1-x2, x2+3x3, x1 - x2+2x3>, , T: R^3 to R^3, T(<x1,x2,x3>) = <2x1-x2, x2+3x3, x1 - x2+2x3>, , bases B = { <1,0,1>, <1,1,0>, <0,1,1> } and B' = { <1,1,-2>, <2,1,-1>, <3,1,1> }. Find T ( <3,-1,2> ) by using...
  5. Z

    Finding a matrix W such that W^t*AW = D (D is diagonal matrix)

    Homework Statement A = 000 010 101 Find Eigenvalues, its corresponding eigenvectors, and find a matrix W such that W^t*AW = D, where D is a diagnol matrix.(note that W^t represents the transpose of W) Homework Equations Eigenvalues, Eigenvectors, diagnolization[/B]The Attempt at a...
  6. A

    Finding the Base Matrix A from Matrix A100

    Homework Statement If A100 is some 3x3 matrix, find the base matrix A. 2. Relevant information Eigenvalues, diagonalization, etc. The Attempt at a Solution So far, I've been finding the eigenvalues and diagonalizing the matrix via A = P-1DP where D is the diagonal matrix and P is a matrix...
  7. Y

    Linear Algebra - Elimination Matrix when Permutation Needed

    Homework Statement I feel like I should know the answer to this, so I believe this to be an easy question. Say have matrix A, and I store the elimination matrices E_1,1 E_2,1 etc. and somewhere in the elimination process I have to use a permutation matrix to swap rows. My question is when I...
  8. P

    QR factorization for a 4x4 tridiagonal symmetric matrix

    Homework Statement $$\begin{bmatrix} a_{11} & a_{12} & 0 & 0\\ a_{12} & a_{22} & a_{23} & 0\\ 0 & a_{23} & a_{33} & a_{34} \\ 0 & 0 & a_{34} & a_{44} \\ \end{bmatrix} = \begin{bmatrix} q_{11} & q_{12} & q_{13} & q_{14} \\ q_{21} & q_{22} & q_{23} & q_{24} \\ q_{31} & q_{32} & q_{33} & q_{34}...
  9. C

    Transformation of a 2x2 matrix with Pauli matrices

    Homework Statement Suppose the vector ##\phi## transforms under SU(2) as: $$\phi' = (\exp(-i \alpha \cdot t))_{ij}\phi_j,$$ where ## (t_j)_{kl} = −i \epsilon_{jkl}## and ##j, k, l \in \left\{1, 2, 3\right\}.## Based on ##\phi,## we define the ##2 \times 2## matrix ##\sigma = \tau \cdot...
  10. kq6up

    I Feynman Lecture Vol III Ch. 8 Question -- Heisenberg matrix picture

    Is the Hamiltonian matrix that is constructed in Ch 8 of the Feynman lectures the Heisenberg matrix picture, or is it something else? I am just curious. Thanks, Chris Maness
  11. M

    MHB Applying rotation matrix to make inclined plane flat again

    I want to rotate an inclined plane to achieve a flat surface. I think I can use the Euler angles to perform this operation. Using following data: and following rotation matrix I think you can make the plane flat by following rotations: 1: rotation around x-axis by 45° 2: rotation around...
  12. D

    I How to Solve for a 3x3 Matrix Using A and B Vectors?

    Hi all, I have this data that can be described by M*A = B, where M is a 3x3 matrix and A and B are 3x1 vectors. Since I know and can collect A and B data, and I have 9 unknowns in the 3x3 matrix, I thought that collecting 9 pairs of A and B vectors would yield the matrix M's coefficients via 9...
  13. H

    I A real matrix and its inverse share the same eigenvectors?

    Suppose ##v_i## is an eigenvector of ##A## with eigenvalue ##\lambda_i## and multiplicity ##1##. ##AA^{-1}v_i=A^{-1}Av_i=A^{-1}\lambda_iv_i=\lambda_iA^{-1}v_i## Thus ##A^{-1}v_i## is also an eigenvector of ##A## with the same eigenvalue ##\lambda_i##. Since the multiplicity of ##\lambda_i##...
  14. D

    Linear Algebra Book about block matrix multiplication

    I still can't find a book with properties and theorems involving block matrices multiplication to reference in my undergraduate work. thanks
  15. D

    Matrix Determinants Homework: Finding the Answer

    Homework Statement Homework EquationsThe Attempt at a Solution The answer in the solutions is given as : (2x+1)(x-1)(1-x), they did their matrix differently so that's how they got that answer. I used wolfram alpha to factorise my quadratic on the last line and it gave me alternative forms...
  16. Kevin McHugh

    I Determinant of a 4x4 matrix

    I know row reduction methods are the best way to calculate the determinant of large matrices. I was wondering if you can use the appended matrix method to calculate the determinant of a 4x4 by appending the matrix with the first 3 columns. There should be n! terms, but I only get 8 instead of 24.
  17. I

    A Eigenstates of "summed" matrix

    Hi to all. Say that you have an eigenvalue problem of a Hermitian matrix ##A## and want (for many reasons) to calculate the eigenvalues and eigenstates for many cases where only the diagonal elements are changed in each case. Say the common eigenvalue problem is ##Ax=λx##. The ##A## matrix is...
  18. Ismail Siddiqui

    [Linear Algebra] Conjugate Transpose of a Matrix and vectors in ℂ

    Homework Statement Let A be an n x n matrix, and let v, w ∈ ℂn. Prove that Av ⋅ w = v ⋅ A†w Homework Equations † = conjugate transpose ⋅ = dot product * = conjugate T = transpose (AB)-1 = B-1A-1 (AB)-1 = BTAT (AB)* = A*B* A† = (AT)* Definitions of Unitary and Hermitian Matrices Complex Mod...
  19. M

    Understanding matrix converter (Venturini's solution)

    Hi, I'm actually trying to do some simulation on matrix converters for my university power electronics subject. I am reading through the different types of modulation techniques. One of them, the Venturini direct approach, with sinusoidal voltage output and input current. I'm having a little...
  20. G

    Matrix of linear transformation

    Homework Statement Let A:\mathbb R_2[x]\rightarrow \mathbb R_2[x] is a linear transformation defined as (A(p))(x)=p'(x+1) where \mathbb R_2[x] is the space of polynomials of the second order. Find all a,b,c\in\mathbb R such that the matrix \begin{bmatrix} a & 1 & 0 \\ b & 0 & 1 \\ c & 0...
  21. C

    Non singular matrix M such that MAM^T=F

    Homework Statement Show that there is a non-singular matrix M such that ##MAM^T = F## for any antisymmetric matrix A where the normal form F is a matrix with 2x2 blocks on its principal diagonal which are either zero or $$\begin{pmatrix} 0 &1 \\ -1&0 \end{pmatrix}$$ To do so, consider the...
  22. dwdoyle

    Degenerate Perturbation Theory and Matrix elements

    Homework Statement I did poorly on my exam, which I thought was very fair, and am now trying to understand certain aspects of perturbation theory. There are a total of three, semi related problems which i have questions about. They are mainly qualitative in nature and involve an intuitive...
  23. R

    I Just to be sure about the Jacobian matrix and determinant....

    Ok, I've got these functions to get the x (right), y (up) and z (forward) coordinates to plot with my computer program: x = r*Math.cos(a)*Math.sin(o) y = r*Math.sin(a) z = -r*Math.cos(a)*Math.cos(o) It's the equations of a sphere where I've placed the origin (o,a,r) = (0,0,0) of the source...
  24. A

    I Conceptual Question: Vector-Matrix Differential Equation

    Hi I'm just having trouble wrapping my head around differential equations with matrices and vectors... For example: let y be a vector. let A(t) be an nxn matrix. I have the differential equation: dy/dt = A(t)y So I think I understand why the solution is y = ceA(t) But I'm having trouble...
  25. CynicusRex

    Infinite solution to system with no free variables?

    Homework Statement The assignment is to find all values of k (in R) for which the system has 0 solutions, 1 solution and infinite solutions. If there are infinite solutions, find the amount of free variables. The system of linear equations: kx + (k+1)y + z = 0 kx + y + (k+1)z = 0 2kx + y + z =...
  26. beyondlight

    Solve derivative of least squares matrix equation

    Homework Statement I am designing a MIMO communication system, with input signal s, channel H and transform matrix T. The received signal is corrupted by noise. Homework Equations [/B] The received signal is r = Hs+n And then it is transformed (compressed) by: y = Tr And then its...
  27. D

    Solving Matrix Equations: Inverse of nxn (n=2)

    Homework Statement Homework Equations Inverse of an (nxn) (n=2 only) square matrix: The Attempt at a Solution The answer provided in the solutions does the exact same thing except, where my ?? are. It does A = BCB^-1. Where as I do A = CBB^-1. When I was doing this question I was...
  28. G

    MHB Linear transformation and its matrix

    1. Show that the map $\mathcal{A}$ from $\mathbb{R}^3$ to $\mathbb{R}^3$ defined by $\mathcal{A}(x,y,z) = (x+y, x-y, z)$ is a linear transformation. Find its matrix in standard basis. 2. Find the dimensions of $\text{Im}(\mathcal{A})$ and $\text{Ker}(\mathcal{A})$, and find their basis for the...
  29. Schwarzschild90

    Transfer matrix for a finite length? (Quantum mechanics)

    Homework Statement I'm struggling to find a solution to exercise (*b). I have uploaded a pdf of the assignment. Please advise me at your convenience. Homework Equations x(x_l^+) = T(x_l^+, x_l^-)x(x_l^-) The Attempt at a Solution x(a^-) = \frac{\psi(a^-)}{\psi(a^-)} , T(a^+, a^-) \left(...
  30. Telemachus

    Find Inverse of Matrix Homework Statement

    Homework Statement I have to find the inverse for this generic matrix (the dimensions are not specified, but I assume its a square matrix, I don't know if that is necessary). ##A=\left [ \begin{matrix} 1 & -1 & -1 & -1 & \dots & -1 & -1 \\ 0 & 1 & -1 & -1 & \dots & -1 & -1 \\ 0 & 0 & 1 & -1...
  31. A

    How to derive the quantum commutation in matrix mechanics?

    Homework Statement I would like to know how to derive the quantum commutation relations in matrix form, $$i \hbar \partial_t x(t)= [x(t),E]$$ $$i \hbar \partial_t P(t)= [P(t),E]$$ Where X(t), P(t) and E are the position, momentum and the energy of the particle, respectively. 2. Homework...
  32. D

    Master Matrix Multiplication: Solving Size Confusion | Homework Help

    Homework Statement Well, basically my issue isn't exactly with how to multiply matrices. I know how to do that, my issue is the way my lecturer shows how to find the size of the new matrix, this is all that he shows: I mean how is he getting AX to be a 3x1 matrix? Homework EquationsThe...
  33. rolotomassi

    Plot 0s & 1s Matrix in GNUplot: Solve "No Usable Data" Error

    I have a .txt file which is 50 rows x 50 columns filled with entirely 0's and 1's. I have tried to plot the data with and without spaces between each column. I keep getting this message: gnuplot> splot 'C:\Users\raf\Desktop\PolymerProject\monte carlo code\directionInitial.txt' with pm3d...
  34. O

    B Application of Matrices and Determinants

    Hello I was learning about determinants and matrices. I learned the generalization of getting the determinant of an n by n matrix. I then applied this to vector space (i + j + k) via a cross product and noticed that you leave the i j and k in their own columns in the first row of the matrix...
  35. S

    Insight/Intuition into rotations in R²

    I've been using rotation matrices for quite some time now without fully grasping them. Whenever I tried to develop an intuitive understanding of... x' = x\cos\theta - y\sin\theta \\ y' = x\sin\theta + y \cos\theta ... I failed and gave up. I've looked at numerous online texts and videos, but...
  36. R

    Linear Algebra matrix linear transformation

    Homework Statement Consider the linear transformation T from V = P2 to W = P2 given by T(a0 + a1t + a2t2) = (−4a0 + 2a1 + 3a2) + (2a0 + 3a1 + 3a2)t + (−2a0 + 4a1 + 3a2)t^2 Let E = (e1, e2, e3) be the ordered basis in P2 given by e1(t) = 1, e2(t) = t, e3(t) = t^2 Find the coordinate matrix...
  37. P

    Is the Induced Weighted Matrix Norm Equal to WAW^-1?

    Homework Statement The weighted vector norm is defined as ##||x||_W = ||Wx||##. W is an invertible matrix. The induced weighted matrix norm is induced by the above vector norm and is written as: ##||A||_W = sup_{x\neq 0} \frac{||Ax||_W}{||x||_W}## A is a matrix. Need to show ##||A||_W =...
  38. D

    Matrix Reflection Homework: Find Orthogonal Matrix in R3 Plane

    Homework Statement Let u1,u2,u3 be an orthonormal basis for R3 and consider M as the plane with equation x1+2x2-2x3=0. Find the matrix of orthogonal reflection in that plane with respect to the given basis. Homework EquationsThe Attempt at a Solution In previous exercises , I had a matrix A...
  39. H

    Converting operator matrix (Quantum Chemistry question)

    Dear all, I want to know how to convert operator matrix when using Dirac Bra-Ket notation when it must be converted into a new dimension. I am currently working on transition dipole moment operator matrix D which I am going to use the following one: D = er Where e is charge of electron, r is...
  40. P

    Finding the Inverse of a 2x2 Matrix using Gauss-Jordan Method

    Homework Statement $$ \begin{bmatrix} a &b \\ c&d \end{bmatrix}$$ I'm supposed to find the inverseHomework Equations Method of Gauss-Jordan The Attempt at a Solution So I tried putting zeros in this and I got the following : $$ \begin{bmatrix} ad-ac &0 &ad &ad-a \\ 0&bc-ad &c &-a...
  41. P

    Linear algebra : Doing a proof with a square matrix

    Homework Statement Show that all square matrix (A whatever) can be written as the sum of a symmetric matrix and a anti symmetric matrix. Homework Equations I think this relation might be relevant : $$ A=\frac{1}{2}*(A+A^{T})+\frac{1}{2}*(A-A^{T}) $$ The Attempt at a Solution I know that we...
  42. G

    Linear algebra: Find the matrix of linear transformation

    Homework Statement Check if L(p)(x)=(1+4x)p(x)+(x-x^2)p'(x)-(x^2+x^3)p''(x) is a linear transformation on \mathbb{R_2}[x]. If L(p)(x) is a linear transformation, find it's matrix in standard basis and check if L(p)(x) is invertible. If L(p)(x) is invertible, find the function rule of it's...
  43. C

    Matrix-Vector Form Write an Augmented Matrix

    Homework Statement Write in Vector-Matrix form then write the augmented matrix of the system. r + 2s + t = 1 r - 3s +3t = 1 4s - 5t = 3 Homework Equations The matrix to which the operations will be applied is called the augmented matrix of the system Ax = b, It is formed by appending the...
  44. G

    The Limit of a Matrix Sequence as n Approaches Infinity

    Homework Statement [/B] Find the limit as ##n \to \infty ## of ##U_n(a) =\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & a/n \\ 0 & -a/n & 1 \end{pmatrix}^n##, for any real ##a##. Homework EquationsThe Attempt at a Solution I find ##U =\begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos a & \sin a \\ 0 & -\sin a &...
  45. P

    Proving Unitary Matrix Norm: $$||UA||_2 = ||AU||_2$$

    Homework Statement Prove $$||UA||_2 = ||AU||_2$$ where ##U## is a n-by-n unitary matrix and A is a n-by-m unitary matrix. Homework Equations For any matrix A, ##||A||_2 = \rho(A^*A)^.5##, ##\rho## is the spectral radius (maximum eigenvalue) where ##A^*## presents the complex conjugate of A. U...
  46. TheMathNoob

    Adjacency matrix and probability matrix

    Homework Statement If Γ is a k-regular simple graph and Γ its directed double, show that the matrix ˜ S for Γ (as per the FEATURED ARTICLE ) is a multiple of the adjacency matrix ˜ for Γ. Find the multiple. Assume k > 1. The matrix S is the probability matrix. The probability of going from one...
  47. Destroxia

    Solve 3x3 Matrix Equation: x, y, z Variables

    Homework Statement Find a 3x3 matrix A that satisfies the following equation where x, y, and z can be any numbers. ## A \begin{vmatrix} x \\ y \\ z \end{vmatrix} = \begin{vmatrix} x + y \\ x - y \\ 0 \end{vmatrix}##Homework EquationsThe Attempt at a Solution I attempted to solve this like...
  48. Fightfish

    Lowest eigenstate of hopping matrix

    So, I was examining the ground state of a Bose-Hubbard dimer in the negligible interaction limit, which essentially amounts to constructing and diagonalizing a two-site hopping matrix that has the form H_{i,i+1}^{(n)} = H_{i+1,i}^{(n)} = - \sqrt{i}\sqrt{n-i+1}, with all other elements zero...
  49. J

    Self-adjoint matrix, general form

    Hi, I am looking for the general form of 2x2 complex transformation matrix. I have the article, that says "the relative position of a self-adjoint 2x2 matrix B with respect to A as a reference (corresponding to the transformation from the eigenspaces of A to the eigenspaces of B) is determined...
  50. I

    How to create a matrix with variables?

    Hello, I am kind of new to Matlab so the questions I will ask probably sound a bit basic. Anyways, here goes: I want to create the matrix below which has both constants and variables. How can I do this? I know how to create a normal matrix (e.g. B = [1 0 2; 3 4 5; 0 2 3]) but I don't know how...
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