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

    I Simplifying a matrix into an equation

    Hi, Please see the attached image. I have a matrix and would like to split it up into a nice compact equation if possible. Matrix A seems to be a nice pattern that would lend itself to writing in equation form but I’m not sure what to do. Is it possible? Also do you know how I could correctly...
  2. M

    I Finding the Matrix O for a 4x4 Operator Acting on a 4x1 Vector

    I have a 4x4 operator O. I apply it on a 4x1 vector A. Let's say A =[0.7; 0.4 ; 0.4; 0.3]. When O acts on A, I get B. Let's say B=[0.74 ; 0.56; 0.08 ; 0.36]. The problem is I don't know how to find O. Can you please help me. My basis are [1 ; 0 ; 0; 0], [0;1 ; 0 ;0] ... and so on. Thanks...
  3. M

    A Interesting Matrix Identity

    Hi all, I've come across an interesting matrix identity in my work. I'll define the NxN matrix as S_{ij} = 2^{-(2N - i - j + 1)} \frac{(2N - i - j)!}{(N-i)!(N-j)!}. I find numerically that \sum_{i,j=1}^N S^{-1}_{ij} = 2N, (the sum is over the elements of the matrix inverse). In fact, I...
  4. T

    A How do I find the change of basis matrix for the JCF of M?

    Let ## \begin{align}M =\begin{pmatrix} 2& -3& 0 \\ 3& -4& 0 \\ -2& 2& 1 \end{pmatrix} \end{align}. ## Here is how I think the JCF is found. STEP 1: Find the characteristic polynomial It's ## \chi(\lambda) = (\lambda + 1)^3 ## STEP 2: Make an AMGM table and write an integer partition...
  5. M

    Proof a property for a 3x3 matrix

    Let a 3 × 3 matrix A be such that for any vector of a column v ∈ R3 the vectors Av and v are orthogonal. Prove that At + A = 0, where At is the transposed matrix.
  6. J

    I Divergence of traceless matrix

    Assume that ##\partial M_{ab}/\partial \hat{n}_c## is completely symmetric in ##a, b## and ##c##. Then, it is stated in the book I read that the divergence of the traceless part of ##M## is proportional to the gradient of the trace of ##M##. More precisely, $$ \partial /\partial \hat{n}_a...
  7. R

    I Beam-splitter transformation matrix

    The transformation matrix for a beam splitter relates the four E-fields involved as follows: $$ \left(\begin{array}{c} E_{1}\\ E_{2} \end{array}\right)=\left(\begin{array}{cc} T & R\\ R & T \end{array}\right)\left(\begin{array}{c} E_{3}\\ E_{4} \end{array}\right) \tag{1}$$ Here, the amplitude...
  8. Haorong Wu

    I Does a unitary matrix have such property?

    Hi. I'm learning Quantum Calculation. There is a section about controlled operations on multiple qubits. The textbook doesn't express explicitly but I can infer the following statement: If ##U## is a unitary matrix, and ##V^2=U##, then ## V^ \dagger V=V V ^ \dagger=I##. I had hard time...
  9. synMehdi

    I Linear least squares regression for model matrix identification

    Summary: I need to Identify my linear model matrix using least squares . The aim is to approach an overdetermined system Matrix [A] by knowing pairs of [x] and [y] input data in the complex space. I need to do a linear model identification using least squared method. My model to identify is a...
  10. chopnhack

    Creating a vectorized statement in MatLab to output a 5x5 Hilbert matrix

    My first attempt was: V=zeros(5,5) a=1; i=1:5; j=1:5; V(i:j)=a./(i+j-1) I figured to create a 5x5 with zeros and then to return and replace those values with updated values derived from the Hilbert equation as we move through i and j. This failed with an error of : Unable to perform assignment...
  11. C

    Matrix Problem: Find A and B such that A = O, B =O, AB= O and BA =O

    Let A= [ a b] [ c d ] B = [ w x] [ y z] Then aw +by=0 bx+dz=0 cw+dy=0 cx+dz=0 aw+cx! =0 bw+x! =0 ya+cz!=0 by+dz! =0 But I don't get the answer after this
  12. lastItem

    I Calculating Momentum Operator Matrix Elements from <φ|dH/dkx|ψ>

    Is there a relationship between the momentum operator matrix elements and the following: <φ|dH/dkx|ψ> where kx is the Bloch wave number such that if I have the latter calculated for the x direction as a matrix, I can get the momentum operator matrix elements from it?
  13. S

    Singular 3x3 Matrix: Solving & Understanding

  14. Kaguro

    Conditions for diagonalizable matrix

    If a 3×3 matrix A produces 3 linearly independent eigenvectors then we can write them columnwise in a matrix P(non singular). Then the matrix D = P_inv*A*P is diagonal. Now for this I need to show that different eigenvalues of a matrix produce linearly independent eigenvectors. A*x = c1x A*y...
  15. C

    Matrix Multiplication -- Commutivity versus Associativity

    According to me matrix multiplication is not commutative. Therefore A^2.A^3=A^3.A^2 should be false. But at the same time matrix multiplication is associative so we can take whatever no. of A's we want to multiply i.e A^5=A.A^4 OR A^5=A^2.A^3
  16. karush

    MHB -pe.7 write a system in the matrix form Y'=AY+G

    nmh{896} mnt{347.21} consider th non-homogeneous first order differential system where $x,y,z$ are all functions of the variable t \begin{align*}\displaystyle x'&=-4x-3y+3z\\ y'&=3x+2y-3z+e^t\\ z´&=-3x-3y+2z \end{align*} write a system in the matrix form $Y'=AY+G$
  17. J

    I The Multiplication Table is a Hermitian Matrix

    I was drawing out the multiplication table in "matrix" form (a 12 by 12 matrix) for a friend trying to pass the GED (yes, sad, I know) and noticed for the first time that the entries on the diagonal are real, i.e. the squares (1, 4, 9, 16, ...), and the off diagonal elements are real and complex...
  18. A

    A Matrix Exponential to Approximate the Value of Matrizant

    Hello, Consider the system of linear homogeneous differential equations of first order dy/dx = A(x) y where x denotes the independent variable, A(x) is a square matrix, and y is an unknown vector-function...
  19. user366312

    How can I find "Limiting Distribution" of the following Markov matrix?

    2nd one is considerably hard to compute ##P^n## using simple matrix multiplication as the given matrix ##P## is cumbersome to work with. Also, I need to know how to test a matrix to find if that matrix has a limiting distribution. So, I need some help.
  20. patric44

    Efficient Solution for Dividing Matrices: B/A Calculation Explained

    he is asking for the division of the two matrices , so i tried to get the inverse of the matrix A but it appears to get more complex as the delta for A is somehow a big equation . and what really bothers me that there is another A , B inside the matrix B ?! find B/A .
  21. S

    MHB Markov chains- Can I have some help creating the transition matrix for this scenario?

    I just discovered this website and want to thank everyone who is willing to contribute some of their time to help me. I appreciate it more than you know First off, assume that state 1 is Chinese and that state 2 is Greek, and state 3 is Italian. A student never eats the same kind of food for 2...
  22. L

    Density matrix of an ammonia molecule

    In ##t = 0##, we have ##\rho (0) = | + \rangle \langle + |##. The time evolution of the density matrix is given by ##\rho(t) = e^{-i\hat{H}t} \rho (0) e^{i\hat{H}t}## (I am considering ##\hbar = 1##). I can write the state ##| + \rangle ## as a linear combination of the eigenstates of the...
  23. A

    A Cluster Decomposition.Vanishing of the connected part of the S matrix.

    Im following Weinberg's QFT volume I and I am tying to show that the following equation vanishes at large spatial distance of the possible particle clusters (pg 181 eq 4.3.8): S_{x_1'x_2'... , x_1 x_2}^C = \int d^3p_1' d^3p_2'...d^3p_1d^3p_2...S_{p_1'p_2'... , p_1 p_2}^C \times e^{i p_1' ...
  24. Mentz114

    I Markov Process: How to Tell Reversibility & Eigenvalues=1

    I refer to the transition matrix for a Markov process and I have two questions 1. How can one tell if a Markov process is reversible ? 2. Can it have two (or more) eigenvalues equal to 1 ? My definition of the matrix is that it should have all rows(or columns) sum to 1. Thanks.
  25. T

    A How to find the Jordan Canonical Form of a 5x5 matrix and its steps?

    To see the steps I have completed so far, https://math.stackexchange.com/q/3168898/261956 I think there are at least three more steps. The next step is finding the eigenvectors together with the generalized eigenvectors of each eigenvalue. Then we use this to construct the transition matrix...
  26. T

    Non-Rotation Matrix Split: Hello

    Hello This could very well be an idiotic question, but here goes... Consider a general matrix M Consider a rotation matrix R (member of SO(2) or SO(3)) Is it possible to split M into the product of a rotation matrix R and "something else," say, S? Such that: M = RS or the sum M = R + S...
  27. P

    Finding the unitary matrix for a beam splitter

    Hello, I have some trouble understanding how to construct the matrix for the beam splitter (in a Mach-Zehnder interferometer). I started with deciding my input and output states for the photon. I then use Borns rule, which I have attached below: To get the following for the state space...
  28. A

    Matrix algebra : Find the matrix C such that N(A) = R(C)

  29. Haorong Wu

    How to diagonalize a matrix with complex eigenvalues?

    Homework Statement Diagonalize the matrix $$ \mathbf {M} = \begin{pmatrix} 1 & -\varphi /N\\ \varphi /N & 1\\ \end{pmatrix} $$ to obtain the matrix $$ \mathbf{M^{'}= SMS^{-1} }$$ Homework Equations First find the eigenvalues and eigenvectors of ##\mathbf{M}##, and then normalize the...
  30. N

    I Block Diagonal Matrix and Similarity Transformation

    I am looking at page 2 of this document.https://ocw.mit.edu/courses/chemistry/5-04-principles-of-inorganic-chemistry-ii-fall-2008/lecture-notes/Lecture_3.pdf How is the transformation matrix, ν, obtained? I am familiar with diagonalization of a matrix, M, where D = S-1MS and the columns of S...
  31. Z

    Example Required: Matrix Solution By Dividing into Quadrants

    Homework Statement Hi, I am looking for an example to solve a larger Matrix by dividing into Quadrant. Is it possible for Gauss Elimination or Matrix Multiplication. Homework Equations No equation possible The Attempt at a Solution Looking for a example Zulfi.
  32. S

    Advice on calculating the determinant for 3x3 Matrix by inspection

    Homework Statement The problem is to calculate the determinant of 3x3 Matrix by using elementary row operations. The matrix is: A = [1 0 1] [0 1 2] [1 1 0] Homework EquationsThe Attempt at a Solution By following the properties of determinants, I attempt to get a triangular matrix...
  33. A

    A The product of a matrix exponential and a vector

    Hello everybody! I was studying the Glashow-Weinberg-Salam theory and I have found this relation: $$e^{\frac{i\beta}{2}}\,e^{\frac{i\alpha_3}{2} \begin{pmatrix} 1 & 0 \\ 0 & -1 \\ \end{pmatrix}}\, \frac{1}{\sqrt{2}}\begin{pmatrix} 0\\ v \\ \end{pmatrix} =...
  34. F

    A Covariance matrix size: 3x3 or 4x4?

    Hello, I follow the post https://www.physicsforums.com/threads/cross-correlations-what-size-to-select-for-the-matrix.967222/#post-6141227 . It talks about the constraints on cosmological parameters and forecast on futur Dark energy surveys with Fisher's matrix formalism. Below a capture of...
  35. karush

    MHB 11.3 Give the matrix in standard basis

    We define the application $T:P_2\rightarrow P_2$ by $$T(p)=(x^2+1)p''(x)-xp'(x)+2p'(x)$$ 1. Give the matrix $\displaystyle\left[T\right]_\infty^\infty$ in the standard basis $\alpha=(x^2,x,1)$ 2 Give the matrix $\displaystyle\left[T\right]_\infty^\infty$ where...
  36. H

    MHB Linear Algebra Rank of a Matrix Problem

    Let A be a n x n matrix with complex elements. Prove that the a(k) array, with k ∈ ℕ, where a(k) = rank(A^(k + 1)) - rank(A^k), is monotonically increasing. Thank you! :)
  37. stephchia

    Finding the linear mapping between homogeneous coordinates

    Homework Statement If I have an affine camera with a projection relationship governed by: \begin{equation} \begin{bmatrix} x & y \end{bmatrix}^T = A \begin{bmatrix} X & Y & Z \end{bmatrix}^T + b \end{equation} where A is a 2x3 matrix and b is a 2x1 vector. How can I form a matrix...
  38. F

    I Cross-correlations: what size to select for the matrix?

    Hello, I am working on Fisher's formalism in order to get constraints on cosmological parameters. I am trying to do cross-correlation between 2 types of galaxy populations (LRG/ELG) into a total set of 3 types of population (BGS,LRG,ELG). From the following article...
  39. M

    I Matrix Decomposition Explained: Simple Illustration

    Can anyone illustrate for me matrix decomposition in a simple way?
  40. V

    How to find the diagonal matrix and it's dominant eigenvalue

    Homework Statement Consider the following vectors, which you can copy and paste directly into Matlab. x = [2 2 4 6 1 5 5 2 6 2 2]; y = [3 3 3 6 3 6 3 2 3 2]; Use the vectors x and y to create the following matrix. 2 3 0 0 0 0 0 0 0 0 0 3 2 3 0 0 0 0 0 0 0 0 0 3 4 3 0 0 0 0 0 0 0 0 0 3 6 6 0...
  41. lpetrich

    A Structure of modulo-integer matrix group GL(r,Z(n))?

    Over in the thread The eight-queens chess puzzle and variations of it | Physics Forums I discovered that with a toroidal board, one with periodic boundary conditions, the amount of symmetries becomes surprisingly large (A group-based search for solutions of the n-queens problem - ScienceDirect)...
  42. lalo_u

    Charge operator applied to matrix multiplets

    In the context of SM (##SU(3)_C\otimes SU(2)_L\otimes U(1)_Y##) the charge operator is ##Q_{SM} = T_3 + \frac{Y}{2}\mathbb{I}_2## and gives us the fermions charges. Here ##T_3=\frac{1}{2}\sigma_3## is the third ##SU(2)## generator. For example, assuming ##Y=-1## for the left lepton doublet...
  43. M

    MHB Check the statements about a 4x5 matrix with rank 2.

    Hey! :o Let $A$ be a $4\times 5$ matrix with rank $2$ and let $U$ be the corresponding row echelon form matrix. I want to check if the following statements are true or not. If $B$ is a $5\times 5$ invertible matrix, at least two of the columns of $B$ are not in the nulity of $A$. There...
  44. TheBigDig

    Spin Annhilation and Creator Operators Matrix Representation

    Homework Statement Given the expression s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1> obtain the matrix representations of s+/- for spin 1/2 in the usual basis of eigenstates of sz Homework Equations s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1> S_{+} = \hbar...
  45. Abhishek11235

    A How to calculate the matrix of a form?

    This is screenshot from V.I Arnold's book on Classical mechanics. My question is how do we find matrix of any n-form. Detailed answer please.
  46. EEristavi

    Solving a System of Equations via the Matrix Method

    I have equation system: x + y + z - a*k = 0 -b*x + y + z = 0 -c*y + z = 0 -d*x + y = 0 where: a, b, c, d = const. Have to find: x, y, z, k Attempt of solution: I create Matrix A with coefficients; Matrix B - Solutions (Zeros) and Matrix X - variables. When I try to use Cramer's rule -...
  47. cookiemnstr510510

    Solving Linear Algebra Problem 8: Gauss-Jordan Method

    Hello All, I have a question regarding the wording of this problem and my method of solving. (Problem and directions attached in Linear.jpg) PROBLEM 8 NOT 7! :) Here is my thought process: Keep doing elementary row operations until we have it it gauss-jordan form, then we have our answers?! I...
  48. cookiemnstr510510

    I How to Write a Matrix on a Webpage?

    Hello, sorry if this is in the incorrect thread but I am wondering how I write a matrix on here? Much help appreciated and more problems to come ;) Thanks!
  49. V

    Solve Matrix A: Homework Equations & Solution

    Homework Statement Solve for the Matrix A. (AT + 4I)-1 = [-1 1, 2 1] Homework EquationsThe Attempt at a Solution I am unsure of how exactly to do this. Here is what I have done: (A-1)T = 1/4I + [-1 1, 2 1] Am I on track? Thank you.
  50. M

    MHB The decomposition for a symmetric positiv definite matrix is unique

    Hey! :o We have the matrix \begin{equation*}A=\begin{pmatrix}1/2 & 1/5 & 1/10 & 1/17 \\ 1/5 & 1/2 & 1/5 & 1/10 \\ 1/10 & 1/5 & 1/2 & 1/5 \\ 1/17 & 1/10 & 1/5 & 1/10\end{pmatrix}\end{equation*} I have applied the Cholesky decomposition and found that $A=\tilde{L}\cdot \tilde{L}^T$ where...
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