Matrix Definition and 121 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. nightingale123

    Finding the Jordan canonical form of a matrix

    Homework Statement About an endomorphism ##A## over ##\mathbb{C^{11}}## the next things are know. $$dim\, ker\,A^{3}=10,\quad dim\, kerA^{2}=7$$ Find the a) Jordan canonical form of ##A## b) characteristic polynomial c) minimal polynomial d) ##dim\,kerA## When: case 1: we know that ##A## is...
  2. M

    SIS epidemics transition matrix

    Homework Statement [/B] The population is 50 The diseases is known to follow SIS dynamics with the following probabilities The number of infected individuals increases with probability 0.1 and it decreases with probability 0.05 the probability that nothing happens is 0.85 a) what is the...
  3. Const@ntine

    Comp Sci 5x5 Arrays - Sum & Difference - (Fortran)

    Homework Statement Create two 5x5 arrays, A & B, and ask the person to fill them out. Save those numbers in matrix_a.txt & matrix_b.txt respectively. Then, save the sum and difference of those numbers in sum.txt & diff.txt respectively. Basically we need to create two arrays, fill them out...
  4. nightingale123

    System of linear equations

    Homework Statement 3.For which values of ##\lambda## does the following system of equations also have non trivial solutions Homework Equations The Attempt at a Solution What I tried doing first is to put all variables on the same side and got ## v+y-\lambda*x=0\\ x+z-\lambda*y=0\\...
  5. B

    I How do i find the eigenvalues of this tough Hamiltonian?

    I have this Hamiltonian --> ( Where each G is a matrix. I want to find the eigenvalues but I'm getting hung up on the fact that there are 6 indices. Each G matrix lives in a different space so I can't just multiply the G matrices together. If I built this Hamiltonain...
  6. M

    Properties of Solutions of Matrix ODEs

    Homework Statement We assume from ODE theory that given a smooth A: I → gl(n;R) there exists a unique smooth solution F : I → gl(n;R), defined on the same interval I on which A is defined, of the initial value problem F' = FA and F(t0) = F0 ∈ gl(n;R) given. (i) Show that two solutions Fi : I...
  7. M

    Proving basic linear ODE results

    Homework Statement Please bear with the length of this post, I'm taking it one step at a time starting with i) Let A: I → gl(n, R) be a smooth function where I ⊂ R is an interval and gl(n, R) denotes the vector space of all n × n matrices. (i) If F : I → gl(n, R) satisfies the matrix ODE F'...
  8. N

    I Trying to understand least squares estimates

    Hi, I'm trying to understand which mathematical actions I need to perform to be able to arrive at the solution shown in the uploaded picture. Thank you.
  9. M

    Prove all Elements of O(2,R) have form of Rotation Matrix

    Homework Statement Show that every matrix A ∈ O(2, R) is of the form R(α) = cos α − sin α sin α cos α (this is the 2d rotation matrix -- I can't make it in matrix format) or JR(α). Interpret the maps x → R(α)x and x → JR(α)x for x ∈ R 2 Homework Equations The Attempt at a Solution So I know...
  10. M

    Linear Algebra: Matlab Question

    I am taking a linear algebra class, and it has a required lab associated with it. Here is the following problem that I must solve using Matlab 1. Homework Statement Write a function using row reduction to find the inverse for any given 2x2 matrix. Name your function your initial + inv(M), the...
  11. MickeyBlue

    Representing a transformation with a matrix

    Homework Statement Use matrix multiplication to find the 2×2 matrix P which represents projection onto the line y =√3x. Can you suggest another way of finding this matrix? Which vectors x∈R2 satisfy the equation Px = x? For which x is Px = 0? Homework Equations Dot product of vectors The...
  12. MrsM

    Using eigenvalues to get determinant of an inverse matrix

    Homework Statement Homework Equations determinant is the product of the eigenvalues... so -1.1*2.3 = -2.53 det(a−1) = 1 / det(A), = (1/-2.53) =-.3952 The Attempt at a Solution If it's asking for a quality of its inverse, it must be invertible. I did what I showed above, but my answer was...
  13. M

    I A regular matrix <=> mA isomorphism

    Hello all Let ##m_A: \mathbb{K^n} \rightarrow \mathbb{K^n}: X \mapsto AX## and ##A \in M_{m,n}(\mathbb{K})## (I already proved that this function is linear) I want to prove that: A regular matrix ##\iff m_A## is an isomorphism. So, here is my approach. Can someone verify whether this is...
  14. S

    I Rotation matrix in 3x3

    Hello! I need to find the rotation matrix around a given vector v=(a,b,c), by and angle ##\theta##. I can find an orthonormal basis of the plane perpendicular to v but how can I compute the matrix from this? I think I can do it by brute force, rewriting the orthonormal basis rotated by...
  15. O

    I On Matrix Multipication

    Hello, I was refreshing my Mathematics using S.M. Blinder's book "Guide to Essential Math" and on the section on Matrix Multiplication I got the following, Can someone elaborate on the highlighted section? In particular, what does "adjacent indices" mean? Thank you.
  16. A

    How do I extract elements of a random matrix masked by a circle with its center at A(15,26)

    Lets say I have a matrix A=rand(31,51). How can I extract its elements from its center (say row = 15, column = 26) in circular manner. I want to have a matrix that displays only those elements of 'A' which are inside a circle with its center at A(15,26). Radius of circle can be any number say 5...
  17. A

    Matrix representation of certain Operator

    Homework Statement Vectors I1> and I2> create the orthonormal basis. Operator O is: O=a(I1><1I-I2><2I+iI1><2I-iI2><1I), where a is a real number. Find the matrix representation of the operator in the basis I1>,I2>. Find eigenvalues and eigenvectors of the operator. Check if the eigenvectors are...
  18. M

    Matrix operations

    Homework Statement [/B] \begin{array}{cc}1 & 1&1\\ 1&1-s&1-s\\-s&1-s&s^2-1\end{array} a)For which values of s does the inverse exist, and why? You should be using row operations and ideally head for reduced row echelon form b) In the process of calculating part a), you will come across a...
  19. Ken Gallock

    I Decomposition of Matrix

    Hi everyone. There is the ##2\times 2## matrix ##B## $$B= \left[ \begin{array}{cc} B_{11} &B_{12} \\ B_{21}&B_{22} \end{array} \right],~B_{ij}\in \mathbb{C} $$ with property $$\vert B_{11}\vert^2 + \vert B_{12}\vert^2=1,$$ $$\vert B_{21}\vert^2 + \vert B_{22}\vert^2=1,$$...
  20. J

    Matrix riccati differential equation using matlab

    Homework Statement Homework Equations The Attempt at a Solution
  21. kelvin490

    MATLAB Append new columns into Excel

    I would like to ask how to use MATLAB to append new columns into existing excel file without altering the original data in the file? In my case I don't know the original number of columns and rows in the file and it is inefficient to open the files one by one and check in practice. Another...
  22. tommyxu3

    I Determinant of A^t A

    I have a problem of proving an identity about determinants. For ##A\in M_{m\times n}(\mathbb{R}),## a matrix with ##m## rows and ##n## columns, prove the following identity. $$|\det(A^tA)|=\sum_{1\le j_1\le ... \le j_n \le m} (det(A_{j_1...j_n}))^2$$ where ##A_{j_1...j_n}## is the matrix whose...
  23. 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...
  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. 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...
  27. 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...
  28. 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. Homework...
  29. A

    Matrix property proof

    Homework Statement Show that no matrix A ∈ M3 (ℝ) exists so that A2 = -I3 Homework Equations The Attempt at a Solution This is from a french textbook of first year linear algebra. I'm quite familiar with properties of matrices but I don't have any idea of how to prove this. Thanks for the help!
  30. brotherbobby

    Orthogonal character of rotation matrix

    I'd like to prove the fact that - since a rotation of axes is a length-preserving transformation, the rotation matrix must be orthogonal. By the way, the converse of the statement is true also. Meaning, if a transformation is orthogonal, it must be length preserving, and I have been able to...
  31. W

    Angle between coupled forces

    Homework Statement The moment of the couple is 600k (N-m). What is the angle A? F = 100N located at (5,0)m and pointed in the positive x and positive y direction -F = 100N located at (0,4)m and pointed in the negative x and negative y direction Homework Equations M = rxF M = D The Attempt...
  32. Diffie Heltrix

    Norm indueced by a matrix with eigenvalues bigger than 1

    Suppose we pick a matrix M\in M_n(ℝ) s.t. all its eigenvalues are strictly bigger than 1. In the question here the user said it induces some norm (|||⋅|||) which "expands" vector in sense that exists constant c∈ℝ s.t. ∀x∈ℝ^n |||Ax||| ≥ |||x||| . I still cannot understand why it's correct. How...
  33. S

    Full rank of a matrix

    Homework Statement Show that the matrix ##A## is of full rank if and only if ##ad-bc \neq 0## where $$A = \begin{bmatrix} a & b \\ b & c \end{bmatrix}$$ Homework Equations The Attempt at a Solution Suppose that the matrix ##A## is of full rank. That is, rank ##2##. Then by the rank-nullity...
  34. T

    Second Quantization Density Matrix

    Homework Statement Homework Equations and attempt at solution I think I got the ground state, which can be expressed as |\Psi \rangle = \prod_{k}^{N}\hat{a}_{k}^{\dagger} |0 \rangle . Then for the density matrix I used: \langle...
  35. P

    Matrix form for a sphere

    What is the basic matrix form for a uniform (unit) sphere centered at the origin? Given a vector that specifies the radii (1,1,1) == (r1,r2,r3), I would like the matrix that implies no rotation (is it [[1,0,0],[0,1,0],[0,0,1]]?) and covers the rest of the necessary parameters. I am testing...
  36. E

    Linear Transformation and isomorphisms

    Homework Statement Suppose a linear transformation T: [P][/2]→[R][/3] is defined by T(1+x)= (1,3,1), T(1-x)= (-1,1,1) and T(1-[x][/2])=(-1,2,0) a) use the given values of T and linearity properties to find T(1), T(x) and T([x][/2]) b) Find the matrix representation of T (relative to standard...
  37. E

    Bases and Coordinates

    Homework Statement Let B1={([u][/1]),([u][/2]),([u][/3])}={(1,1,1),(0,2,-1),(1,0,2)} and B2={([v][/1]),([v][/2]),([v][/3])}={(1,0,1),(1,-1,2),(0,2,1)} a) Show that B1 is a basis for [R][/3] b) Find the coordinates of w=(2,3,1) relative to B1 c)Given that B2 is a basis for [R[/3], find...
  38. B

    Evaluate the partial derivative of a matrix element

    Homework Statement A determinant a is defined in the following manner ar * Ak = Σns=1 ars Aks = δkr a , where a=det(aij), ar , Ak , are rows of the coefficient matrix and cofactor matrix respectively. The second term in the equation is the expansion over the columns of both matrices, δkr is...
  39. H

    Kronecker function products - matrix format

    Hi all, Firstly, I am not sure whether this is the area of the forum to ask this. I have been learning and researching a completely different topic, and from this I have come across a completely new concept of the Kronecker function. I have done a google search on this to get the intro and...
  40. B

    How Potts model hamiltonian is equal to hamiltonian matrix

    /How can I show that Potts model hamiltonian is equal to this matrix hamiltonian? Potts have these situations : { 1 or 1 or 1 or 0 or 0 or 0} but the matrix hamiltonian : { 1 or 1 or 1 or -1/2 or -1/2 or -1/2} I take some example and couldn't find how they can be equal.
  41. C

    Corresponding Eigenvectors

    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?
  42. 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...
  43. 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...
  44. 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...
  45. 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...
  46. 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...
  47. 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...
  48. ognik

    Angular momentum of rigid body elements tensor

    Homework Statement I was working through my text on deriving the tensor for Angular momentum of the sums of elements of a rigid body, I follow it all except for one step. Here is a great page which shows the derivation nicely - I follow clearly to the...
  49. B

    Comp Sci Output format of a matrix in Fortran 90

    Hello, I'm new here and I'm also new in programming. I never did it before and now I have a problem with one of the programs in fortran 90 and I can't figure out how to solve it. Maybe some of you can help me. Many thanks in advance. 1. Homework Statement I need to plot the results of a...
  50. blue_leaf77

    Subspace of a 4x4 matrix space

    Homework Statement This question is taken from Linear Algebra Done Wrong by Treil. Question 7.5 of chapter 1 says this: What is the smallest subspace of the space of 4 4 matrices which contains all upper triangular matrices (aj,k = 0 for all j > k), and all symmetric matrices (A = AT )? What is...