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

    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...
  2. 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...
  3. 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...
  4. 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...
  5. 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...
  6. 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...
  7. H

    Operator r is a diagonal matrix in position representation

    What does it mean by "In the position representation -- in which r is diagonal" in the paragraph below? How can we show that? Does it mean equation (3) in http://scienceworld.wolfram.com/physics/PositionOperator.html? (where I believe the matrix is in the ##|E_n>## basis)
  8. onkel_tuca

    Solution of a certain NxN matrix, when N->∞

    Hello fellow nerds, I've come across a math problem, where I'd like to find the solution vector of a NxN square matrix. It is possible to find a solution for a given N, albeit numbers in the matrix become very large for any N>>1, and numbers in the solution vector become very small. So it's not...
  9. Hepth

    Minimizing Chi^2, Singular Matrix problem

    I want to construct a completely correlated chi^2. I have a two-dimensional dataset, and its basically like: {m1,m2,m3,m4} {a1,a2,a3,a4} {x0,x0,x0,x0} So m1-m4, a1-a4 are all different, but each x0 is the same. This happens when I am fitting 2D data, but it is required that the function goes...
  10. N

    Hamiltonian matrix for two electrons in a 1D infinite well

    Hi everyone, I need help for preparing a Hamiltonian matrix. What will be the elements of the hamiltonian matrix of the following Schrodinger equation (for two electrons in a 1D infinite well): -\frac{ħ^{2}}{2m}(\frac{d^{2}ψ(x_1,x_2)}{dx_1^{2}}+\frac{d^{2}ψ(x_1,x_2)}{dx_2^{2}}) +...
  11. C

    Question about induced matrix norm

    The induced matrix norm for a square matrix ##A## is defined as: ##\lVert A \rVert= sup\frac{\lVert Ax \rVert}{\lVert x \rVert}## where ##\lVert x \rVert## is a vector norm. sup = supremum My question is: is the numerator ##\lVert Ax \rVert## a vector norm?
  12. TheMathNoob

    Graph theory (incidence matrix and linear algebra)

    Homework Statement I can't understand this paper. I understand the whole incidence matrix stuff, but I don't quiet get how it relates to the linear algebra. I don't know if this is allowed to do, but I will ask you questions line by line, so basically you will read the paper with me explaining...
  13. Kernul

    How do I calculate the bases for Im(f) and Ker(f)?

    Homework Statement Being f : ℝ4 → ℝ4 the endomorphism defined by: ƒ((x, y, z, t)) = (3x + 10z, 2y - 6z - 2t, 0, -y+3z+t) Determine the base and dimension of Im(ƒ) and Ker(ƒ). Complete the base you chose in Im(ƒ) into a base of R4. Homework Equations Matrix A: $$\begin {bmatrix} 3 & 0 & 10 &...
  14. A

    Calculating Square Root of a Matrix in Quantum Information Theory

    I'm doing an online course in quantum information theory, but it seems to require some knowledge of linear algebra that I don't have. A definition that popped up today was the definition of the absolute value of a matrix as: lAl = √(A*A) , where * denotes conjugate transpose. Now for a...
  15. C

    Can an orthogonal matrix be complex?

    Can an orthogonal matrix involve complex/imaginary values?
  16. V

    LinAlg: Determine the value(s) of h such that the matrix....

    Homework Statement Determine the values of h such that the matrix is the augmented matrix of a consistent linear system. 1 4 -2 3 h -6 The attempt at a solution The answer I got differs from the back of the book. I tried solving it by adding R1(4) to R2 1 3 -2 -4 h 8 becomes 1...
  17. mishima

    Understanding Truss Analysis: Investigating the Accuracy of a Bridge Design App

    Hi, my high school students enjoy using the applet found here (http://pages.jh.edu/~virtlab/bridge/truss.htm) to design model (basswood) bridges for our annual regional contest. It seems to require firefox these days. Recently, some designs have been causing extremely large forces to be...
  18. RJLiberator

    Comp Sci C++ (ROOT) Form a matrix and send it to a 2d Histogram

    Homework Statement [/B] 1. I've been tasked with forming a 10 x 10 matrix with elements 0, 1, 2, 3, 4, 5,... and have it display properly. 2. Then, take this matrix and make a 2d-histogram out of it. Homework Equations Here is my code void matrix6( const int n = 10) { float I[n][n]; //...
  19. Linder88

    Determine Diagonalizability of LTI System A

    Homework Statement Consider the LTI (A,B,C,D) system $$ \dot{x}= \begin{pmatrix} 0.5&0&0&0\\ 0&-2&0&0\\ 1&0&0.5&0\\ 0&0&0&-1 \end{pmatrix} x+ \begin{pmatrix} 1\\ 1\\ 0\\ 0 \end{pmatrix} u $$ $$ y= \begin{pmatrix} 0&1&0&1 \end{pmatrix} x $$ Determine if A is diagonalizable Homework EquationsThe...
  20. Y

    MHB Finding Eigenvalues of Matrix A: Wrong Answer, What Am I Doing Wrong?

    Hello all, I have a matrix A and I am looking for it's eigenvalues. No matter what I do, I find that the eigenvalues are 0, 1 and (k+1), while the answer of both the book and Maple is 0 and (k+2). I tried two different technical approaches, both led to the same place. The matrix is...
  21. T

    Matrix elements of non-normalizable states

    Although strictly quantum mechanics is defined in ##L_2## (square integrable function space)， non normalizable states exists in literature. In this case, textbooks adopt an alternative normalization condition. for example, for ##\psi_p(x)=\frac{1}{2\pi\hbar}e^{ipx/\hbar}## ##...
  22. B

    Can a 3x3 Matrix Represent a Quadratic, Cubic, or Quartic Function?

    I have a doubt... Look this matrix equation: \begin{bmatrix} A\\ B \end{bmatrix} = \begin{bmatrix} +\frac{1}{\sqrt{2}} & +\frac{1}{\sqrt{2}}\\ +\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{bmatrix} \begin{bmatrix} X\\ Y \end{bmatrix} \begin{bmatrix} X\\ Y \end{bmatrix} = \begin{bmatrix}...
  23. Raptor112

    Matrix Representation for Combined Ladder Operators

    Due to the definition of spin-up (in my project ), \begin{eqnarray} \sigma_+ = \begin{bmatrix} 0 & 2 \\ 0 & 0 \\ \end{bmatrix} \end{eqnarray} as opposed to \begin{eqnarray} \sigma_+ = \begin{bmatrix} 0 & 1 \\ 0 & 0 \\ \end{bmatrix} \end{eqnarray} and the annihilation operator is...
  24. F

    Find the Eigenvalues and Eigenvectors of 4x4 Matrix.

    Homework Statement X= 1st row: (0, 1, 0, 0), 2nd row: (1, 0, 0, 0), 3rd row: (0, 0, 0, 1-i), 4th row: (0, 0, 1+i, 0) Find the eigenvalues and eigenvectors of the matrix X. Homework Equations |X-λI|=0 (characteristic equation) (λ is the eigenvalues, I is the identity matrix) (X-λI)V=0 (V is the...
  25. J

    Density Matrix and State Alpha

    There is something that I don't quite understand or want clarification. See John Wheeler article "100 years of the quantum" http://arxiv.org/pdf/quant-ph/0101077v1.pdf refer to page 6 with parts of the quotes read "so if we could measure whether the card was in the alpha or beta-states, we...
  26. S

    Linear Transformation: Find the matrix

    Homework Statement Let A(l) = [ 1 1 1 ] [ 1 -1 2] be the matrix associated to a linear transformation l:R3 to R2 with respect to the standard basis of R3 and R2. Find the matrix associated to the given transformation with respect to hte bases B,C, where B = {(1,0,0) (0,1,0) , (0,1,1) } C =...
  27. DuckAmuck

    Matrix Exponential to a Matrix

    If we have two square matrices of the same size P and Q, we can put one in the exponent of the other by: M = P^Q = e^{ln(P)Q} ln(P) may give multiple results R, which are square matrices the same size as P. So then we have: M = e^{RQ} which can be Taylor expanded to arrive at a final square...
  28. evinda

    MHB Solve problem- Identity matrix

    Hello! (Wave) I want to solve the following linear programming problem: $$\min (5y_1-10y_2+7y_3-3y_4) \\ y_1+y_2+7y_3+2y_4=3 \\ -2y_1-y_2+3y_3+3y_4=2 \\ 2y_1+2y_2+8y_3+y_4=4 \\ y_i \geq 0, i \in \{ 1, \dots, 4 \}$$ $\begin{bmatrix} 1 & 1 & 7 & 2 & | & 3\\ -2 & -1 & 3 & 3 & | & 2\\ 2 & 2 & 8...
  29. H

    Matrix representation of operators

    Let the operators ##\hat{A}## and ##\hat{B}## be ##-i\hbar\frac{\partial}{\partial x}## and ##x## respectively. Representing these linear operators by matrices, and a wave function ##\Psi(x)## by a column vector u, by the associativity of matrix multiplication, we have...
  30. L

    Why Do Different Definitions of Rotation Matrices Exist in Mathematics?

    Happy new year. Why everybody uses this definition of rotation matrixR(\theta) = \begin{bmatrix} \cos\theta & -\sin\theta \\[0.3em] \sin\theta & \cos\theta \\[0.3em] \end{bmatrix} ? This is clockwise rotation. And we always use counter clockwise in...
  31. H

    Matrix representation of an operator with a change of basis

    Why isn't the second line in (5.185) ##\sum_k\sum_l<\phi_m\,|\,A\,|\,\psi_k><\psi_k\,|\,\psi_l><\psi_l\,|\,\phi_n>##? My steps are as follows: ##<\phi_m\,|\,A\,|\,\phi_n>## ##=\int\phi_m^*(r)\,A\,\phi_n(r)\,dr## ##=\int\phi_m^*(r)\,A\,\int\delta(r-r')\phi_n(r')\,dr'dr## By the closure...
  32. H

    Tensor & Matrix: Cartesian Vector & Transformation Rule?

    Each set of constant numbers such as ##(v_1, v_2, v_3)## are the components of a constant Cartesian vector because by rotation of coordinates they satisfy the transformation rule. Can we consider each set of constant arrays ## a_{ij};i,j=1,2,3 ## as components of a Cartesian tensor? In other...
  33. S

    Decoherence in the long time limit of density matrix element

    For a state |\Psi(t)\rangle = \sum_{k}c_k e^{-iE_kt/\hbar}|E_k\rangle , the density matrix elements in the energy basis are \rho_{ab}(t) = c_a c^*_be^{-it(E_a -E_b)/\hbar} How is it that in the long time limit, this reduces to \rho_{ab}(t) \approx |c_a|^2 \delta_{ab} ? Is there some...
  34. B

    LaTeX How can matrices be written in Latex with or without vertical lines?

    How do you write a matrix such as below image in Latex, in this forum?
  35. evinda

    MHB Is the Matrix Positive Definite?

    Hello! (Wave) We have that $q(x) \geq q_0>0, x \in [0,1], h>0$. Suppose that we have this $(N+1) \times (N+1) matrix$: $\begin{bmatrix} \frac{1}{h^2}+\frac{1}{h}+\frac{q(x_0)}{2} & -\frac{1}{h^2} & 0 & \cdots & 0 \\ -\frac{1}{h^2} & \frac{2}{h^2}+q(x_1) & -\frac{1}{h^2} & \cdots &0 \\ 0 &...
  36. perplexabot

    When is the gram matrix positive definite?

    Hey all. I know that A^TA is positive semidefinite. Is it possible to achieve a positive definite matrix from such a matrix multiplication (taking into account that A is NOT necessarily a square matrix)?
  37. S

    When a matrix isn't diagonalizable

    Homework Statement Determine if the matrix is diagonalizable or not. A= [ 3 -1 ] [ 1 1 ] Homework Equations Eigenvalues = det(A-Iλ) determinant of a 2x2 matrix = ad-bc The Attempt at a Solution Eigenvalues = det(A-Iλ) [ 3 -1 ] - [ λ 0 ] = [ 3 -λ -1 ] [ 1 1 ] [ 0 λ ]...
  38. Fredrik

    Insights Matrix Representations of Linear Transformations - Comments

    Fredrik submitted a new PF Insights post Matrix Representations of Linear Transformations Continue reading the Original PF Insights Post.
  39. S

    Matrix of a Linear Transformation Example

    Homework Statement Hi this isn't really a question but more so understanding an example that was given to me that I not know how it came to it's conclusion. This is a question pertaining linear transformation for coordinate isomorphism between basis. https://imgur.com/a/UwuACHomework Equations...
  40. Martin V.

    Understanding the Role of Matrix Multiplication in Solving Equations

    Hello hope you can help me. Can anybody tell me what goes on from equation 3 to 4. especially how gets in?
  41. RJLiberator

    Inner product propety with Scalar Matrix (Proof)

    Homework Statement Let A be an nxn matrix, and let |v>, |w> ∈ℂ. Prove that (A|v>)*|w> = |v>*(A†|w>) † = hermitian conjugate Homework EquationsThe Attempt at a Solution Struggling to start this one. I'm sure this one is likely relatively quick and painless, but I need to identify the trick...
  42. D

    Diagonalizing a Matrix: Steps and Verification

    Homework Statement Diagonalize matrix using only row/column switching; multiplying row/column by a scalar; adding a row/column, multiplied by some polynomial, to another row/column. Homework EquationsThe Attempt at a Solution After diagonalization I get a diagonal matrix that looks like...
  43. Corwin_S

    What is the Jones Matrix of a mirror at an angle?

    Hi, Concerning optical polarization, what is the Jones Matrix of a mirror at a non-zero angle of incidence with respect to incoming light? For a mirror at normal incidence the matrix is (1 0; 0 -1); How do I incorporate the angle?
  44. TheSodesa

    Finding the eigenvectors of a matrix A

    Homework Statement A = \begin{bmatrix} 2 & 1 & 0\\ 0& -2 & 1\\ 0 & 0 & 1 \end{bmatrix} Homework EquationsThe Attempt at a Solution The spectrum of A is \sigma (A) = { \lambda _1, \lambda _2, \lambda _3 } = {2, -2, 1 } I was able to calculate vectors v_1 and v_3 correctly out of the...
  45. C

    How many hadamard matrix matrices exists for size n?

    Homework Statement How many hadamard matrices exists for size n? Homework Equations Hadamard matrices are square matrices whose entries are either +1 or −1 and whose rows are mutually orthogonal. The Attempt at a Solution I am just curious how many exists for 4, 8 and in general.[/B]
  46. piJohn1411

    Mathematica Is it possible to colour the rows or columns of a matrix?

    Hi, I was wondering if it's possible to colour the rows and columns of a matrix in mathematica. I have received help from another forum and the code of my matrix is the following: Rasterize@ Style[MatrixForm[{{n, -1 + n, -2 + n, \[CenterEllipsis], 1}, {2 n, 2 n - 1, 2 n - 2...
  47. Amith2006

    Quark mixing factor in CKM matrix

    I find that the quark mixing factor say for example ##V_{ub}## is the same for: u ##\Leftrightarrow## b ##u\Leftrightarrow\bar{b}## ##\bar{u}\Leftrightarrow## b ##\bar{u}\Leftrightarrow\bar{b}## Does this have something to do with weak interaction being unable to distinguish these from one...
  48. kostoglotov

    Backwards difference matrix divided by negative delta x?

    An exercise in my text requires me to (in MATLAB) generate a numeric solution to a given second order differential equation in three different ways using a forwards, centered and backwards difference matrix. I got reasonable answers for \vec{u} that agreed with each other (approximately) for the...
  49. N

    Do Both HHH and HHH Follow the Same Complex Wishart Distribution?

    Hello, Assume that H is a n \times m matrix with i.i.d. complex Gaussian entries each with zero mean and variance \sigma. Also, let n>=m. I ' m interested in finding the relation between the distribution of HHH and HHH, where H stands for the Hermittian transposition. I anticipate that both...
  50. ognik

    MHB Exploring the 3-D Rotation Matrix with Euler Rotations and Net Angle of Rotation

    The question mentions an orthogonal matrix describing a rotation in 3D ... where $\phi$ is the net angle of rotation about a fixed single axis. I know of the 3 Euler rotations, is this one of them, arbitrary, or is there a general 3-D rotation matrix in one angle? If I build one, I would start...
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