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. U

    Matrix Solutions: Find Linearly Independent Solutions

    Homework Statement given the matrix https://scontent.fhlz2-1.fna.fbcdn.net/v/t1.15752-9/40882602_313421129235428_2500668957757800448_n.png?_nc_cat=0&oh=7f5d6372c263996c6a11969b072d1349&oe=5BF8F2B7 in RREF we see solution to this system is x1+x2+x3 = 0 in the textbook it says which solutions...
  2. T

    MHB Matrix solutions with variable coefficient

    Hey guys, I've got this question, that I think I have figured out, but I'm not completely sure. Basically, I've got the following matrix to put into RREF. Not really a problem, but I'm not sure if I'm handling the variable incorrectly. $\begin{bmatrix} 1 &-1 &|1 \\ 3 &a &|3 \end{bmatrix}$...
  3. P

    I Why do you need infinite size matrix which commute....

    ...to give a number? https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/lecture-notes/MIT8_04S16_LecNotes5.pdf On page 6, it says, " Matrix mechanics, was worked out in 1925 by Werner Heisenberg and clarified by Max Born and Pascual Jordan. Note that, if we were to write xˆ...
  4. R

    MHB Differential equation with a matrix

    Suppose we have the matrix $ \mathbf{N} = \begin{bmatrix} 4 & -2 \\ -2 & 1 \end{bmatrix}$ and $\mathbf{X} = \begin{bmatrix}x \\ y \end{bmatrix}$. I want to solve $\displaystyle \frac{d\mathbf{X}}{dt} = \mathbf{NX}$. The eigenvalues of the matrix are $\lambda_1, \lambda_2 = 0,5$ and eigenvectors...
  5. opus

    B Can elementary matrix operations change the solutions to a system of equations?

    To my understanding, a matrix is just a way of representing a system of equations in an organized format. So for example, if we have some system of equations, we can get them into standard form, and translate them into what's known as an augmented matrix. This is similar to using synthetic...
  6. G

    I On the Coriolis Forcing vector and its Matrix

    The context for the question is in the attachments (pg1.png, pg2.png, pg3.png), so there is some reading involved. Although, it is a short and simple read if anything. The inquiry is in (inquiry.png). My understanding of the situation is that Q(t) abides by the differential equation Q'(t)Q(t)T...
  7. C

    MHB Finding the Rotation Matrix for 60 Degree Rotation around (1,1,1) Axis

    Dear Everybody, I am having some problem with one exercise. And the question states: Find the transformation Matrix R that describes a rotation by 60 degrees about an axis from the origin thru the pt (1,1,1). The rotation is clockwise as you look down toward the origin. I know the standard...
  8. C

    MHB Two dimensional rotational Matrix

    Dear Everybody, I am trying to learn about the electrodynamics. I am using the textbook, Introduction to Electrodynamics (2nd Ed) by D. J. Griffiths. I am working on the Problem 1.8. The question state: Prove that the two-dimensional rotation matrix perverse the length of A. (That is, show...
  9. N

    Unitary transformation using Python

    I would like to ask about unitary transformation. UA(IV) UB*UA(IV) UAT(UB*UA(IV))=UB(IV) UB(IV)*(X) IVT(UB(IV)*(X))=UB(X) UBT*UB(X)=X From the information above, UAT,IVT and UBT are the transpose of the complex conjugate. The aim of this code is to get the value of X in the step 4. This is...
  10. N

    Polarization of light using Mueller matrix

    Hi everyone First of all, I am a computer science student and I have a question regarding the polarization of light as stated in an article entitled "Multi-stage quantum secure communication using polarization hopping" by Rifai et al.,2015. Given the Mueller matrix: The input of light state is...
  11. R

    MHB Is there a formula that gives me the RREF of a matrix?

    Is there formula that transforms a matrix into its row-reduced echelon form? I know I can get there by row operations. But isn't there be like a formula?
  12. L

    A The hermicity of a k.p matrix?

    I am trying to use the k.p method to study quantum well band structure. One example Hamiltonian look like this [J. Appl. Phys., 116, 033709(2014)] where ##{{\hat k}_ \pm } = {{\hat k}_x} \pm i{{\hat k}_y}## and the matrix elements are function of ##{{\hat k}_i}## and if quantum well is grown...
  13. Abhishek11235

    Proving the following properties

    Mentor note: Member warned that an attempt must be shown. 1. Homework Statement This question is from book Afken Weber, Mathematics for Physicist. An operator ##T(t + ε,t)## describes the change in the wave function from t to t + ##\epsilon## . For ##\epsilon## real and small enough so that...
  14. Y

    Fortran How to use Real Array Index in Matrix dimension?

    I am developing a FORTRAN code (.f90) which "ll calculate some matrix in some time interval (dt1=0.001) and these matrices have to be integrated in some time steps (dt=0.1). Though I am experience in FORTRAN 77, new to FORTRAN 90. I am unable to make dimension of matrix real (I think that is the...
  15. B

    Non-negative matrix factorization code

    Hello, I'm looking for the non-negative matrix factorization (NNMF) source code. I checked several linear algebra libraries (e.g., LaPack, mkl), but it seems that this subroutine is not available. Does anyone know where I can find this source code...
  16. B

    Create Row-Orthonormal Matrix | m > n

    Hello, I'm looking for a way to create an approximate row-orthonormal matrix with the number of rows (m) > the number of columns (n); i.e., finding A(mxn) so that A(mxn) . A^T(nxm) = I(mxm). I used singular value decomposition (e.g., DGESVD in mkl mathlib), but what I actually got was an...
  17. Mutatis

    Write the matrix representation of the raising operators....

    Homework Statement Hi, guys. The question is: For a 3-state system, |0⟩, |1⟩ and |2⟩, write the matrix representation of the raising operators ## \hat A, \hat A^\dagger ##, ## \hat x ## and ##\hat p ##. Homework Equations I know how to use all the above operators projecting them on...
  18. snoopies622

    B Can a matrix be transformed like a vector?

    Suppose I have a vector space V and a matrix M such that multiplying every vector in V by M creates another vector space W. Now suppose I have another matrix A that I can also use to change vectors in V into other vectors. Does there exist a third matrix B such that - for any vector v1 in V -...
  19. KF33

    How Do You Solve Matrix Equations with a Calculator?

    Homework Statement Homework EquationsThe Attempt at a Solution I know I would have to do something with my calculator and I tried to solve like solving an equation for C, but not sure. I put all the matrices in my calculator. I then subtracted the first matrix to the other side then...
  20. L

    A How was the matrix in the attachment found

    I understand the dot product of ei.ej, but I can't find the matrix components.
  21. E

    A Matrix coordinates of D branes

    Can someone explain to me how is it possible for D-branes to be parametrized with matrix coordinates? I mean, D-brane is a surface embedded in ordinary space, no? And the coordinates of ordinary space are vectors. So how can those vector coordinates suddenly turn into matrix ones on a D-brane?
  22. Aleoa

    Probability of Hall in H after John's Second Play: Markov Matrix Solution

    Mentor note: Thread moved from Mathematics section, so is missing the HW template John and Eli are playing a game with a hall that can roll into one of two pockets labelled H and Y. John wants to keep the hall in H and Eli wants to keep it in Y. When it is John's turn to play, ifhe finds the...
  23. AwesomeTrains

    Density matrix for a mixed neutron beam

    Homework Statement A beam of neutrons (moving along the z-direction) consists of an incoherent superposition of two beams that were initially all polarized along the x- and y-direction, respectively. Using the Pauli spin matrices: \sigma_x = \begin{pmatrix} 0 & 1 \\ 1 & 0 \\...
  24. D

    Stiffness matrix for elastic materials

    For an anisotropic material, is there any way to analytically determine the elements of the stiffness matrix? For orthotropic and isotropic materials, there are analytical expressions relating the stiffness matrix elements to the elastic modulus and poisson's ratio, but I do not believe this...
  25. Michael Sullivan

    ABCD matrix for an optical system of two thick lenses

    Homework Statement I have an object at distance x1 from the first thick lens(convex) then air at distance x2 to the next thick lens(concave) then air of distance x3 to a mirror. I need to build an ABCD matrix representing this. Homework Equations thick lens equation: [ A B ] = [ 1-d/R1...
  26. M

    Find the standard matrix of the linear transformation

    Homework Statement Homework Equations None. The Attempt at a Solution I know that the standard matrix of a counterclockwise rotation by 45 degrees is: [cos 45 -sin 45] [sin 45 cos 45] =[sqrt(2)/2 -sqrt(2)/2] [sqrt(2)/2 sqrt(2)/2] But the problem says "followed by a projection onto the line...
  27. S

    I Eigenproblem for non-normal matrix

    I understand that a normal matrix has a complete, canonical eigendecomposition in which the normalized modal eigenvector matrix is unitary, and this its inverse is simply the transpose, and the modal eigenvalue matrix is diagonal (let's presume distinct eigenvalues). But I wonder if there is...
  28. Aleoa

    Construct a 2x2 nilpotent matrix

    Homework Statement Costruct a: The Attempt at a Solution I found 3 equations but i miss another one :( M=\begin{bmatrix} a & b\\ c & d \end{bmatrix} (1) a+d = 0 from the definition of nilpotent matrix (2) a+3b = 0 from kernel (3) c +3d= 0 from kernel
  29. L

    A Eigenvalues and matrix entries

    If matrix has integer entries and it is hermitian, are then eigenvalues also integers? Is there some theorem for this, or some counter example?
  30. Aleoa

    Construct a 2x2 matrix that expresses a given transformation

    Homework Statement I have to costruct a 2x2 matrix so that : The Attempt at a Solution M =\begin{bmatrix} a & b\\ c &d \end{bmatrix} Using the first bond i got : c+2d = 2a+4b (1) using the second bond : d = -b (2) And then, as a nilpotent matrix has det = 0 and tr = 0, i got a+d-2=0 (3)...
  31. L

    Setting up a matrix from a linear equation

    Homework Statement I need some help with a question on my assignment. It asks to set up a matrix from the linear equations, y=25x+70 and y=35x+40. Homework Equations How do I set this matrix up? The Attempt at a Solution I think that I have to rewrite it as 25x-y=-70 and 35x-y=-40. But then I...
  32. L

    Why Is My Matrix Not Diagonal After Transformation?

    Homework Statement Form unitary matrix from eigen vectors of ##\sigma_y## and using that unitary matrix diagonalize ##\sigma_y##. \sigma_y= \begin{bmatrix} 0 & -i & \\ i & 0 & \\ \end{bmatrix}[/B]Homework Equations Eigen vectors of ##\sigma_y## are...
  33. D

    I Can You Add a Scalar to a Matrix Directly?

    So, I recently came across this example: let us "define" a function as ƒ(x)=-x3-2x -3. If given a matrix A, compute ƒ(A). The soution proceedes in finding -A3-2A-3I where I is the multiplicative identity matrix. Now , I understand that you can't add a scalar and a matrix, so the way I see it is...
  34. snoopies622

    B How does matrix non-commutivity relate to eigenvectors?

    Given matrices A,B and Condition 1: AB does not equal BA Condition 2: A and B do not have common eigenvectors are these two conditions equivalent? If not, exactly how are they related? Since I'm thinking about quantum mechanics I'm wondering specifically about Hermitian matrices, but I'm...
  35. S

    I Proving only 1 normalized unitary vector for normal matrix

    AIUI, every normal matrix has a full eigenvector solution, and there is only 1 *normalized* modal matrix as the solution (let's presume unique eigenvalues so as to avoid the degenerate case of shared eigenvalues), and the columns of the modal matrix, which are the (normalized) eigenvectors, are...
  36. Ben Geoffrey

    I Lorentz Transformation Matrix: Tensor of Order 2?

    Is the Lorentz transformation matrix Λμν a tensor of order two and does it transform like a tensor ?
  37. bornofflame

    [Linear Algebra] Construct an n x 3 matrix D such that AD=I3

    Homework Statement Suppose that A is a 3 x n matrix whose columns span R3. Explain how to construct an n x 3 matrix D such that AD = I3. "Theorem 4" For a matrix A of size m x n, the following statements are equivalent, that is either all true or all false: a. For each b in Rm, Ax = b has a...
  38. M

    Mathematica How to Add Matrices Along Diagonals

    Hi PF! Let's say I have a 3X3 matrix ##K## and a much larger square matrix, call it ##M##. I am trying to add ##K## into ##M## along the diagonals. It's difficult for me to explain (and hence code) so I've attached a picture. Does anyone know a good way of doing this? Notice overlap is only in...
  39. karush

    MHB Find the inverse of matrix (q2)

    $\textsf{Find the inverse of matrix} $ $$A=\left| \begin{array}{rrr} 1&0&2\\ 1&0&0 \\ 3&2&0 \end{array} \right|$$ $\textsf{by method of adjoint matrix }\\$ $\textsf{adj $A = |C_{ij}|^T$}\\$ $\textsf{det $A =4$}\\$ $\textsf{so then}\\$ $A^{-1}=\frac{1}{det A}(adj A)= \frac{1}{4}(adj A)$...
  40. D

    I How Do Indices Determine Positions in a Quantum Density Matrix?

    I am reading Leonard Susskind's Theoretical Minimum book on Quantum Mechanics. Excercise 7.4 is as follows: Calculate the density matrix for ##|\Psi\rangle = \alpha|u\rangle + \beta|d\rangle##. Answer: $$ \psi(u) = \alpha, \quad \psi^*(u) = \alpha^* \\ \psi(d) = \beta, \quad \psi^*(d) =...
  41. R

    Matrix representation relative to bases

    Homework Statement Please see attached file. I'm not quite sure if I'm on the right track here. I think the basis for F is throwing me off as well as T(f). Please advise. Thanks! Homework EquationsThe Attempt at a Solution
  42. A

    MHB Derivation of an inequality from the paper “A CLT For A Band Matrix Model” by Anderson's and Zeitoun

    I am trying to see how to derive the following inequality on page 36 in the proof of Lemma 11.3: https://arxiv.org/pdf/math/0412040.pdf I.e, of: $$\| fg \|_{Lip} \le \bigg(1+\ell \sup_{t\in T} |g'(t)|\bigg)\sup_{t\in T}|f'(t)| , \ \ supp \ f(1-g)\subset S^c$$ My thoughts about how to show...
  43. F

    Linear algebra matrix to compute series

    Post moved by moderator, so missing the homework template. series ##{a_n}## is define by ##a_1=1 ## , ##a_2=5 ## , ##a_3=1 ##, ##a_{n+3}=a_{n+2}+4a_{n+1}-4a_n ## ( ##n \geq 1 ##). $$\begin{pmatrix}a_{n+3} \\ a_{n+2} \\ a_{n+1} \\ \end{pmatrix}=B\begin{pmatrix}a_{n+2} \\ a_{n+1} \\ a_{n} \\...
  44. Come

    Eigenvalues/eignevectors of Jones matrix

    I did an exercice for an optic course and the question was to find which optical component, using eigenvalues and eigenvectors, the following Jones matrix was (the common phase is not considered) : 1 i i 1 I found that this is a quarter-wave plate oriented at 45 degree from the incident...
  45. L

    Linear Algebra - Find an orthogonal matrix P

    A problem that I have to solve for my Linear Algebra course is the following We are supposed to use Mathematica. What I have done is that I first checked that A is symmetric, i.e. that ##A = A^T##. Which is obvious. Next I computed the eigenvalues for A. The characteristic polynomial is...
  46. mertcan

    Jacobian matrix and Navier Stokes equation

    Hi, in first attachment/picture you can see the generalized navier stokes equation in general form. In order to linearize these equation we use Beam Warming method and for the linearization process we deploy JACOBİAN MATRİX as in the second attachment/picture. But on my own I can ONLY obtain the...
  47. A

    Stiffness matrix for a symmetric structure

    Good day All While trying to solve the following exercice, I was stucked by a couple of issues for the first part in which we have to find the simplest configuration ( symmetry) according to my basic understanding Symmetry must be : geometry load support here I don t have the third...
  48. A

    Stiffness Matrix Issue: Get Help Now!

    Good day All, while trying to solve this exercice I was puzzeld by the solution approach indeed, they use the symmetry of the structure, they have made a cut on the hinge where the force F is applied (the force F has been divided by 2 for the symmetry reason), and ONLY replace it with a...
  49. Dethrone

    MHB Layout Notation for matrix calculus

    Hi, I guess this could be a rather silly question, but I got a bit confused about the "numerator layout notation" and "denominator layout notation" when working with matrix differentiation...
  50. P

    I Orthogonal matrix construction

    Given a real-valued matrix ## \bar{B}_2=\begin{bmatrix} \bar{B}_{21}\\ \bar{B}_{22} \end{bmatrix}\in{R^{p \times m}} ##, I am looking for an orthogonal transformation matrix i.e., ##T^{-1}=T^T\in{R^{p \times p}}## that satisfies: $$ \begin{bmatrix} T_{11}^T & T_{21}^T\\ T_{12}^T...
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