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. J

    Find a 3x3 Matrix such that....

    Homework Statement Find a non zero matrix(3x3) that does not have in its range. Make sure your matrix does as it should.The Attempt at a Solution [/B] I know a range is a set of output vectors, Can anyone help me clarify the question? I'm just not sure specifically what its asking of me, in...
  2. B

    Is matrix hermitian and its eigenvectors orthogonal?

    I calculate 1) ##\Omega= \begin{bmatrix} 1 & 3 &1 \\ 0 & 2 &0 \\ 0& 1 & 4 \end{bmatrix}## as not Hermtian since ##\Omega\ne\Omega^{\dagger}## where##\Omega^{\dagger}=(\Omega^T)^*## 2) ##\Omega\Omega^{T}\ne I## implies eigenvectors are not orthogonal. Is this correct?
  3. J

    Find a 2x2 Matrix which performs the operation....

    Homework Statement [/B]Find the matrix that performs the operation 2x2 Matrix which sends e1→e2 and e2→e1Homework EquationsThe Attempt at a Solution [/B] I know e1 = < 1 , 0> and e2 = <0 , 1> Basically I'm not quite sure what the question is asking. This is the one of the problems I am...
  4. A

    A proof related to 2 X 2 matrix

    Let A be a 2 X 2 matrix such that AX = XA for all 2 X 2 real matrices X. Show that A =kI for some k belonging to R
  5. S

    What is a Centered Difference Matrix?

    A difference matrix takes the entries of a vector and computes the differences between the entries like [x1 - 0 ] = difference from 0 and x1: 1 step [x2 - x1] = difference from x2 and x1: 1 step [x3 - x2] = difference from x3 and x2: 1 step assuming we had a vector x in Ax = b So why now when...
  6. Digitalism

    New Sci-Fi Series: Babylon 5 & Matrix Creators' Latest

    It's a new series on Netflix from those involved with Babylon 5 and the Matrix. Has anyone here seen it yet? What did you think about it?
  7. A

    Diagonalising an n*n matrix analytically

    Hi everyone I am trying to diagonalise a (2n+1)x(2n+1) matrix which has diagonal terms A_ll = (-n+l)^2 and other non vanishing terms are A_l(l+1) = A_(l+1)l = constant. Is there any way I can solve it for general n without having to use any numerical methods. I remember once a professor...
  8. ChrisVer

    Problem with calculating the cov matrix of X,Y

    If I have two random variables X, Y that are given from the following formula: X= \mu_x \big(1 + G_1(0, \sigma_1) + G_2(0, \sigma_2) \big) Y= \mu_y \big(1 + G_3(0, \sigma_1) + G_2(0, \sigma_2) \big) Where G(\mu, \sigma) are gaussians with mean \mu=0 here and std some number. How can I find...
  9. C

    Are Both Eigenvectors Correct?

    say for example when I calculate an eigenvector for a particular eigenvalue and get something like \begin{bmatrix} 1\\ \frac{1}{3} \end{bmatrix} but the answers on the book are \begin{bmatrix} 3\\ 1 \end{bmatrix} Would my answers still be considered correct?
  10. A

    Matrix Equation: Finding Non-Zero Solution for AX + XA = 0

    Homework Statement Let A be the matrix \left(\begin{array}{cc}a&b\\c&d\end{array}\right), where no one of a, b, c, d is zero. It is required to find the non-zero 2x2 matrix X such that AX + XA = 0, where 0 is the zero 2x2 matrix. Prove that either (a) a + d = 0, in which case the general...
  11. L

    Derive parameters from transform matrix

    Hello everybody, Sorry to ask you something that may be easy for you but I'm stuck. For example I have 2 images (size 2056x2056). One image of reference and the other is the same rotated from -90degrees. Using a program with keypoints, it gives me a transform matrix : a=2.056884522e+03...
  12. B

    MHB Matrix Ops: R(x)v & R(x)w Rotate Counter-Clockwise

    I have the following matrix R(x) = [cos(x) -sin(x) ; sin(x) cos(x)] Now consider the unit vectors v = [1;0] and w = [0,1]. Now if we compute R(x)v and R(x)w the vectors are supposed to rotate about the origin by the angle x in a counter clockwise direction. I am struggling to see how this...
  13. S

    Can someone explain to me what a matrix is in simple words?

    Ok so officially a matrix is a rectangular array of numbers, symbols, etc arranged in rows and columns that is treated in certain prescribed ways. But that doesn't help me understand a darn thing. From what I understand, a matrix is a math tool that can help you solve linear systems, represent...
  14. JesseJC

    Solving a matrix of ones and zeros

    Homework Statement _ _ |1 0 0 0 -1 0 0 | 700 | |0 1 0 0 -1 0 0 | 500 | |0 0 1 0 0 0 0 0 | 150 | |0 0 0 1 0 1 0 | 1200 | |0 0 0 0 1 0 0 | -650 | |0 0 0 0 0 0 1 | -600 | Homework EquationsThe Attempt at a Solution This is driving me up the wall, am I missing...
  15. A

    How to formulate nonsingularity of matrix (I + A*B) in LMIs?

    Consider I+A*B where A: (n*l) is a variable matrix and B: (l*n) is known. I am looking for some way to find a sufficient condition for nonsingularity of I+A*B
  16. K

    Dynamical matrix and dispersion

    Dear all, In this paper: http://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.125402 In the appendix the author attempts to arrive at the spectral density of states of the surface of a half-space. To do this, he arrives at the Green's function of the surface atom of 1D atomic chain and...
  17. R

    Seesaw mass matrix and neutrino masses

    Hi Since a few days I've been confused about the seesaw mass matrix explaining neutrino masses. It is the following matrix: \begin{pmatrix} 0 & m\\ m & M \\ \end{pmatrix}. As can easily be checked it has two eigenvalues which are given by M and -m^2/M in the limit M>>m (the limit doesn't...
  18. A

    Reason for just a 0 vector in a null space of a L.I matrix

    Hello Everyone, Can someone explain why do matrices with linearly independent columns have only 0 vector in their null space? Thanks
  19. S

    MHB Adjacency Matrix Problem and Alphabet Problem

    Could some please tell me if they think my answer for 1c and 3d of these questions I've done are right. thanks.
  20. I

    Determinant and symmetric positive definite matrix

    As a step in a solution to another question our lecture notes claim that the matrix (a,b,c,d are real scalars). \begin{bmatrix} 2a & b(1+d) \\ b(1+d)& 2dc \\ \end{bmatrix} Is positive definite if the determinant is positive. Why? Since the matrix is symmetric it's positive definite if the it...
  21. H

    Linear Transformations and matrix representation

    Assume the mapping T: P2 -> P2 defined by: T(a0 + a1t+a2t2) = 3a0 + (5a0 - 2a1)t + (4a1 + a2)t2 is linear.Find the matrix representation of T relative to the basis B = {1,t,t2} My book says to first compute the images of the basis vector. This is the point where I'm stuck at because I'm not...
  22. M

    Root and exponent of matrix

    Homework Statement I. 3*3 matrix A (8 2 -2, 2 5 4, -2 4 5) II. 3*3 matrix (1 2 0, -1 -2 0, 3 5 1) Homework Equations I. Solve Aexp 100 of 3*3 II. Find the 5th rooth of B matrix The Attempt at a Solution I. I got stuck at diagonalising the matrix. Is this OK 1st step ? If yes...
  23. J

    Reduced Density Matrix Entropy in 1D Spin Chain

    Good afternoon all, I'm investigating typical values of entropy for a subsystem of a 1D (non-interacting) spin chain. Most of the problem is essentially solved I've shown that a typical pure state of the entire chain is close (trace norm) to the state ##\Omega_S## when reduced. \Omega_S =...
  24. mhsd91

    The Matrix Exponent of the Identity Matrix, I

    So, essentially, all I wonder is: What is the The Matrix Exponent of the Identity Matrix, I? Silly question perhaps, but here follows my problem. Per definition, the Matrix Exponent of the matrix A is, e^{A} = I + A + \frac{A^2}{2} + \ldots = I + \sum_{k=1}^{\infty} \frac{A^k}{k!} =...
  25. Shawnyboy

    Matrix with fractions for indices?

    Hi PF Peeps! Something came up while I was studying for my QM1 class. Basically we want to represent operators as matrices and in one case the matrix element is defined by the formula : <m'|m> = \frac{h}{2\pi}\sqrt{\frac{15}{4} - m(m+1)} \delta_{m',m+1} But the thing is we know m takes on...
  26. C

    How to Make the System Consistent: Solving for Alpha in an Augmented Matrix

    Homework Statement \begin{array}{rrr|r} -1 & 2 & -1 & -3 \\ 2 & 3 & α-1 & α-4 \\ 3 & 1 & α & 1 \end{array} α∈ℝ for the augmented matrix, what value of α would make the system consistent? Homework Equations N/A Answer: α=2 The Attempt at a Solution I know that the system has to have an...
  27. A

    How to calculate density matrix for the GHZ state

    The GHZ state is: |\psi> = \frac{|000> + |111>}{\sqrt2} To calculate density matrix we go from: GHZ = \frac{1}{2}(|000> + |111>)(<000| + <111|) GHZ = \frac{1}{2}( |000><000| + |111><111| + |111><000| + |000><111|) To: GHZ = 1/2[ \left( \begin{array}{cc} 1 & 0 & 0 & 0 & 0 &...
  28. A

    Operators change form for density matrix equations?

    Imagine applying an operator to a wave-function: \psi_t(x_1, x_2, ..., x_n) \rightarrow \frac{L_n(x)\psi_t(x_1, x_2, ..., x_n)}{||\psi_t(x_1, x_2, ..., x_n)||} Where ## \psi _t(x_1, x_2, ..., x_n) ## is initial system state vector, denominator is normalization factor, and Ln(x) is a...
  29. W

    Nullspaces relation between components and overall matrix

    Homework Statement If matrix ## C = \left[ {\begin{array}{c} A \\ B \ \end{array} } \right]## then how is N(C), the nullspace of C, related to N(A) and N(B)? Homework Equations Ax = 0; x = N(A) The Attempt at a Solution First, I thought that the relation between A and B with C is ## C = A...
  30. C

    How Do You Solve for X in a Matrix Equation?

    Homework Statement Given the matrices A, B, C, D, X are invertible such that (AX+BD)C=CA Find an expression for X. Homework Equations N/A Answer is A^{-1}CAC^{-1}-A^{-1}BD The Attempt at a Solution I know you can't do normal algebra for matrices. So this means A≠(AX+BD)?
  31. K

    Holographic Universe. 2D Universe = Matrix?

    Hi people. I just read some articles about physicist starting to gain more and more evidence for the Universe to be a 3D Hologram of a 2D world (or that's how I understood it). And apparently for us living in a "Matrix", like the one in the movie. Now I would like to understand the relation...
  32. R

    How does row operation on an augmented matrix result in the inverse of a matrix?

    I just couldn't understand how does augmented matrix deduce inverse of a matrix. I mean what is it in the row operation because of which we get the inverse of a matrix. I just don't want to learn the steps but to understand why it works. Thank you.
  33. J

    What would it take to fully simulate a physical system?

    Many people out there today seem to think that we'll soon have computers powerful enough to simulate the physical world well enough that we'll be able to upload ourselves and live in such a simulation. People really seem to think a Matrix situation is possible. Some, like Nick Bostrom, have...
  34. binbagsss

    Verify eigenvalues of a TST matrix

    Homework Statement I have ##A=TST(-1,2-1),## and I need to show that an eigenvector of A is,##Y_{j}=sin(kj \pi / J).## and then find the full set of eigenvalues of A. The matrix A comes from writing ##-U_{j-1}+2U-U_{j+1}=h^{2}f(x_{j}), 1\le j \le J-1##, in the form ##AU=b## Homework...
  35. R

    A manipulative matrix question

    Homework Statement If A and B are 2 matrices such that AB = A and BA =B, then B2 is equal to B A Zero matrix I Homework Equations We can pre or post multiply a matrix on both sides of equation. The Attempt at a Solution (AB).(BA) = A.B AB2A = A.B Pre multiply both sides by A-1 We get B2A = AB...
  36. F

    E^A matrix power series (eigen values, diagonalizable)

    Homework Statement Find an expression for e^A with the powerseries shown in the image linked Homework Equations I know you have to use eigen values and eigen vectors and a diagonal matrix The Attempt at a Solution What I did was just try to actually multiply out the infinite series given. I...
  37. D

    How to solve a very large overdetermined system numerically?

    I am doing a project on image processing and I need to solve the following set of equations: nx+nz*( z(x+1,y)-z(x,y) )=0 ny+nz*( z(x+1,y)-z(x,y) )=0 and equations of the boundary (bottom and right side of the image): nx+nz*( z(x,y)-z(x-1,y) )=0 ny+nz*( z(x,y)-z(x,y-1) )=0 nx,ny,nz is the...
  38. binbagsss

    System of first order equations, matrix form, quick question

    Question: ##h_{t}+vh_{x}+v_{x}h=0## ##v_{t}+gh_{x}+vv_{x}=0## Write it in the form ##P_{t}+Q_{x}=0##, where ##P=(h,hv)^{T}##, where ##g## is a constant ##>0##, and ##v## and ##h## are functions of ##x## and ##t##. Attempt: I have ##Q=(vh,?)^{T}##, the first equation looks easy enough, but...
  39. K

    What is wrong with my matrix inversion?

    Homework Statement Find the inverse of the matrix: 1 1 -1 2 -1 1 1 1 2 Homework Equations One must be aware of the identity matrix, as well as how add one row to another with matrix multiplication, for example, the matrix 1 0 0 k 1 0 0 0 1 would add k times the first row to the second...
  40. T

    Understanding Rotation Matrices: A Journey of Mistakes and Lessons Learned

    I'm working through Meisner Thorne and Wheeler (MTW), but have been temporarily sidetracked by a problem with rotation matrices. I've worked through the maths and produced the matrices by multiplying the three individual rotation matrices, (no problem there) but I have been trying to work out...
  41. J

    4x4 Matrix Eigenvalues and Eigenvectors

    Homework Statement I have 4 equations. 3x+6y-5z-t=-8 6x-2y+3z+2t=13 4x-3y-z-3t=-1 5x+6y-3z+4t=-6 I have already solved this matrix using gauss elimination and found that x=1, y=2, z=5, t=-2 Now the next part of the question asks to solve the matrix using eigenvalues and eigenvectors...
  42. B

    How do you get a matrix from this basis?

    Homework Statement Here's my problem. I only need help with the bottom part, but if you could explain the problem more vividly that would help too. Homework Equations A = S-1BS (?) There aren't really any relevant equations. This part of linear algebra is getting really abstract, at least I...
  43. A

    SVD of a reduced rank matrix still has non-zero U and V`?

    In a given matrix A, the singular value decomposition (SVD), yields A=USV`. Now let's make dimension reduction of the matrix by keeping only one column vector from U, one singular value from S and one row vector from V`. Then do another SVD of the resulted rank reduced matrix Ar. Now, if Ar is...
  44. baby_1

    ABCD Matrix of transmison line

    Hello I want to obtain ABCD matrix element value.At first I tried to find A element value with boundary conditions but I don't know how can I find relationship between V(1)+ and V(1)- . Any help appreciate
  45. R

    Statement on matrix and determinant

    Homework Statement If A is a square matrix of order 3 then the true statement is 1. det(-A) = - det A 2.det A = 0 3.det ( A + I) = I + detA 4.det(2A) = 2detA Homework Equations NA The Attempt at a Solution 2. option is obviously not true. Making a random matrix A and verifying properties 1. ...
  46. H

    Linear Combination Mapping: Is the Invertible Matrix Theorem True or False?

    True or False: If the linear combination x -> Ax maps Rn into Rn, then the row reduced echelon form of A is I. I don't understand why this is False. My book says it is false because it is only true if it maps Rn ONTO Rn instead of Rn INTO Rn. What difference does the word into make?
  47. D

    Symmetry of Orthogonally diagonalizable matrix

    Can someone confirm or refute my thinking regarding the diagonalizability of an orthogonal matrix and whether it's symmetrical? A = [b1, b2, ..., bn] | H = Span {b1, b2, ..., bn}. Based on the definition of the span, we can conclude that all of vectors within A are linearly independent...
  48. S

    MHB Solving System of ODEs: Matrix Form, Eigenvalues/Vectors

    Getting stuck on something I think that could be trivial. Maybe someone can see my mistake. consider the system: $x' = -2x + y$ and $y' = 2x - 3y$ a) Write the system in matrix form my solution $\overrightarrow{X} = (^x_y)$ so: $X' = (^{x'}_{y'})$ so $A = $ \begin{bmatrix} -2 & 1 \\ 2 & -3...
  49. P

    Given the basis of find the matrix

    Homework Statement Not a homework problem. Typically, we are given a matrix, then asked to find the basis for the kernel or image space of the matrix. I've never seen a problem that did the converse (i.e., given the matrix for the kernel/image space of some matrix, find some matrix). I was...
  50. arivero

    Has B-L some role in the mass matrix?

    So, B-L is a U(1) generator extracted out of some unified theories of leptons and quarks and in such theories it is traceless, with B=1/3 and L=1, and the trace taken over a "four coloured" multiplet, namely a lepton and three colored quarks. Now, I am amazed that there is another Matrix that...
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