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. 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...
  2. S

    Calculating Matrix Representation of Linear Function in New Basis

    Homework Statement Let ##f : \mathbb{R}^n \rightarrow \mathbb{R}^m## be a linear function. Suppose that with the standard bases for ##\mathbb{R}^n## and ##\mathbb{R}^m## the function ##f## is represented by the matrix ##A##. Let ##b_1, b_2, \ldots, b_n## be a new set of basis vectors for...
  3. S

    Full Rank Matrix: Determinant Condition | Rank-Nullity Theorem

    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 EquationsThe Attempt at a Solution Suppose that the matrix ##A## is of full rank. That is, rank ##2##. Then by the rank-nullity...
  4. S

    Charge conjugation matrix and Dirac equation's solutions

    I saw this somewhere but I think it is wrong... I already read Griffiths' "Introduction to Particle Physics" (the 1st edition) from the page 216 to the page 222 (chapter of Quantum Electrodynamics - section "Solution to the Dirac Equation") and I didn't understood why was there the imaginary...
  5. kostoglotov

    What is this Matrix question asking me to do?

    It's from the chapter on Matrix Inverses... imgur link: http://i.imgur.com/8OhFzgi.jpg This is the entirety of the exercise. It's not following on from or setting anything else up. That's just number 42...what can I do with this?
  6. FOIWATER

    Can the Induced Matrix Norm be Proven with Triangle Inequality?

    Hi, I found a statement without a proof. It seems simple enough, but I am having trouble proving it because I am not positive about induced matrix norms. The statement is that $$||A^k|| \leq||A||^{k}$$ for some matrix A and positive integer k. I have found that the norm of a matrix is the...
  7. 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...
  8. N

    S matrix Unitarity Proof, pg 298 Peskin Schroeder

    I have a question regarding a derivation in Peskin and Schroeder's QFT book. On page 298, he is discussing a method for defining a gauge invariant S matrix. He does this by defining projection operators ##P_0## that project general particle states into gauge invariant states, and then defining...
  9. B

    Degree of liberty of a matrix 2x2

    How many degree of liberty exist, actually, in a matrix 2x2 ? I think that is three! Because the conic equation can be wrote like this: \begin{bmatrix} A & B\\ C & D \end{bmatrix} :\begin{bmatrix} x^2 & xy\\ yx & y^2 \end{bmatrix} + \begin{bmatrix} E\\ F \end{bmatrix} \cdot \begin{bmatrix}...
  10. gfd43tg

    ODE 45 with coupled ODE's in a matrix, reactor temp.

    Homework Statement My question is regarding part (e), I just gave all the questions for reference. Homework EquationsThe Attempt at a Solution These are the coupled equations I should solve (from part d) My issue is using ode45 to get ##C_{A}(t)##, ##C_{P}(t)##, and ##T(t)##. Here is my...
  11. RJLiberator

    Proving Matrix Transformation Property

    Homework Statement Let A and B be n x m matrices, and λ and μ be real numbers. Prove that: (λA+μB)^T = λA^T+μB^t Homework Equations :/ The Attempt at a Solution I'm struggling to start here. If there was no λ and μ, I think I'd be able to reasonably solve this. How do I show that these...
  12. C

    Can the entries of a Matrix be elements of an unordered set?

    Most definitions of a matrix that I have seen involve entries that are elements of a field. What if I have a unorderd set with no operations defined on it, say a set of different colored marbles or a set of historical events. Can I have a matrix whose entries are elements of such a set?
  13. RJLiberator

    Find All Possible Matrix Inverses

    Homework Statement Find 2x2 matrices A and B, all of whose entries are \begin{align} &\geq 0 \end{align}, such that A^-1 and B^-1 exist, but (A+B)^-1 does not exist. Homework Equations The insverse is defined as 1/determinat(matrix) * adj(matrix) Otherwise shown as...
  14. kostoglotov

    How are the x1 and x4 values determined in the solution to the matrix equation?

    Hi, rapid fire posting in this subforum I know, sorry if that's annoying. Let me know if I should space my posts out a bit more. Here's an image of the solution to a worked example (from Intro to Linear Algebra 4th by Strang) here's the imgur link: http://i.imgur.com/IG6r15H.jpg I cannot...
  15. E

    Determinant of 3x3 matrix equal to scalar triple product?

    The determinant of a 3x3 matrix can be interpreted as the volume of a parallellepiped made up by the column vectors (well, could also be the row vectors but here I am using the columns), which is also the scalar triple product. I want to show that: ##det A \overset{!}{=} a_1 \cdot (a_2 \times...
  16. P

    Matrix Representation of a Uniform Sphere Centered at the Origin

    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...
  17. D

    Lorentz transformation matrix and its inverse

    Given the Lorentz matrix Λuv its transpose is Λvu but what is its transpose ? I have seen ΛuaΛub = δb a which implies an inverse. This seems to be some sort of swapping rows and columns but to get the inverse you also need to replace v with -v ? Also In the LT matrix is it the 1st slot...
  18. 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...
  19. E

    Bases and Coordinates: B1 and B2 for [R][/3] - Homework Statement

    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...
  20. B

    How to form the transformation matrix for this

    We were asked to form the transformation matrix that rotates the x1 axis of a rectangular coordinate system 60 degrees toward x2 and the x3 axis. The thing is, I don't understand what it meant by rotating one axis toward the two other. Like, do I rotate x1 60 degrees toward the x2-x3 plane or...
  21. 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...
  22. G

    Dynamic allocation of adjacency matrix and traversing a list

    Homework Statement I have a binary tree. I need to print a path of a doubly circular linked list (0 and 1) after every user input. I have a code in which user inputs data about one person. For example, when user inputs 2 elements, the path should be 0->1. In my code, it won't print any path...
  23. Y

    A system of equations that I want to do with a matrix

    Homework Statement Below are four equations, with the known quantities listed. Solve these equations to obtain an expression for ##T## in terms of known quantities only. Do the same to obtain an expression for ##a## ##T-f=m_1a\hspace{5mm}N-m_1g\cos\theta=0## ##m_2g-T=m_2a \hspace{5mm} f=\mu N##...
  24. SteliosVas

    Expressing Matrix Power as linear combination

    Homework Statement Okay I am given a matrix A = [2 1 ; 3 4] The first step is to find numbers of a and b such that A2 + aA + bI = [0 0; 0 0] I is an identity matrix (2x2). Part B - After that is says to use the result of the above to express A5 as a linear combination of A and I Homework...
  25. duc

    Method to solve a coupled system of matrix equation

    Hello everyone, I'm struggling with a coupled of matrix equations of the general form: AX + CY = cX BY + DX = cY where A, B, C and D are hermitics square matrices. X, Y and c are the eigenvector and eigenvalue to be found. I'm looking for a method or an algorithm to solve this system by using...
  26. R

    Kalman filter a posteriori estimate covariance matrix

    I am having some trouble deriving the a posteriori estimate covariance matrix for the linear Kalman filter. Below I have shown my workings for two methods. Method one is fine and gives the expected result. Method two is the way I tried to derive it initially before further expanding out terms to...
  27. B

    MATLAB Want gray scale image of a matrix in matlab

    I am creating a gray-scale image of a 2000*2000 matrix using mat2gray and imshow command.But highest number of matrix entries that imshow can implement is 500*500 approximately.After that it shows------ "Warning: Image is too big to fit on screen; displaying at 8% > In...
  28. JonnyMaddox

    Hamilton Operator for particle on a circle -- Matrix representation....

    Hey JO. The Hamiltonian is: H= \frac{p_{x}^{2}+p_{y}^{2}}{2m} In quantum Mechanics: \hat{H}=-\frac{\hbar^{2}}{2m}(\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial x^{2}}) In polar coordinates: \hat{H}=-\frac{\hbar^{2}}{2m}( \frac{\partial^{2}}{\partial r^{2}}+\frac{1}{r}...
  29. JesseJC

    Given vectors, constructing a matrix

    Homework Statement Say you've been given vectors v1, v2 and v3. Homework EquationsThe Attempt at a Solution How do I construct a matrix out of these three vectors? Am I to use the given vectors as columns or rows in a matrix? When does this matter and when does it not? This may be a stupid...
  30. T

    Get matrix A from a series of elementary matrices

    1. Get A from its inverse3. I believe it has something to do with the theorem that states: E1E2E3...EkA=I
  31. S

    Linear transformation 2 x 2 matrix problem

    Homework Statement [/B] Find a 2 x 2 matrix that maps e1 to –e2 and e2 to e1+3e2Homework Equations [/B] See the above notesThe Attempt at a Solution [/B] I am making a pig's ear out of this one. I think I can get e1 to –e2 3 -1 1 -3 but as far as getting it to reconcile a matrix like...
  32. O

    IMSL diagonalizing a general complex matrix (DEVCCG)

    Under some circumstances, whenever I call DEVCCG to diagonalize a general complex matrix, the program gets stuck inside and never returns. I do not even get out an error code so that I may continue with the rest of the program. I assume the iterative diagonalization inside the procedure does not...
  33. Anchovy

    Understanding SU(5) gauge boson matrix?

    I have questions regarding the 24 gauge bosons of the SU(5) model. I keep seeing this matrix popping up in the documents I'm reading with no real explanation of why: First of all I'm wondering how this is constructed, which means I'm wondering what the V_{\mu}^{a} look like (I already have...
  34. Lagraaaange

    Linear Algebra vs Matrix Algebra? Which to pick

    In my school LA requires a pre req proof class vs matrix algebra which doesn't. Would matrix algebra even be worth taking?
  35. 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...
  36. J

    Find a 2x2 Matrix with given EigenValues

    Homework Statement Find a 2X2 matrix that has all non-zero entries where 3 is an eigenvalue Homework EquationsThe Attempt at a Solution well since the 2x2 matrix cannot be triangular, it makes things harder for me. I have no idea where to start. I am not given any eigenvectors either. It seems...
  37. I

    Possible Values for K in Powers of Matrix

    Homework Statement A square matrix ##n\times n##, A, that isn't the zero-matrix have powers ##A^{k-1}## that isn't the zero matrix. ##A^k## is the zero matrix. What are the possible values for ##k##? Homework Equations N/A The Attempt at a Solution I'm a bit lost here but I figure that maybe...
  38. M

    Sakurai Question regarding density matrix

    Homework Statement Sakurai Modern Quantum Mechanics Revised Edition. Page 81. density matrix p = 3/4 [1 0; 0 0] + 1/4 [1/2 1/2; 1/2 1/2]. We leave it as an exercise to the reader the task of showing this ensemble can be decomposed in ways other than 3.4.24Homework Equations 3.4.24 w( sz +...
  39. G

    Proof of Nilpotent Matrix: Strictly Upper Triangular Matrices

    Homework Statement Show that strictly upper triangular ##n\times n## matrices are nilpotent. Homework EquationsThe Attempt at a Solution Let ##f## be the endomorphism represented by the strict upper triangular matrix ##M## in basis ##{\cal B} = (e_1,...,e_n)##. We have that ##f(e_k) \in...
  40. ELB27

    Proving a certain orthogonal matrix is a rotation matrix

    Homework Statement Let ##U## be a ##2\times 2## orthogonal matrix with ##\det U = 1##. Prove that ##U## is a rotation matrix. Homework EquationsThe Attempt at a Solution Well, my strategy was to simply write the matrix as $$U = \begin{pmatrix} a & b\\ c & d \end{pmatrix}$$ and using the given...
  41. santos2015

    Rotation matrix between two orthonormal frames

    I am reading a paper and am stuck on the following snippet. Given two orthonormal frames of vectors ##(\bf n1,n2,n3)## and ##(\bf n'1,n'2,n'3)## we can form two matrices ##N= (\bf n1,n2,n3)## and ##N' =(\bf n'1,n'2,n'3)##. In the case of a rigid body, where the two frames are related via...
  42. R

    Skew-symmetric matrix property

    This page (https://shiyuzhao.wordpress.com/2011/06/08/rotation-matrix-angle-axis-angular-velocity/), gives the following relation: \left[R\vec{\omega}\right]_{\times}=R\left[\vec{\omega}\right]_{\times}R^{T} Where: * ##R## is a DCM (Direction Cosine Matrix) * ##\vec{v}## is the angular...
  43. ChrisVer

    CKM matrix and meson oscillations [book]

    Do you know any books or reviews that explains these in sufficient detail? I am having some small problems in understanding the triangles of the CKM matrix elements and experiments conducted for their measurement...
  44. A

    Is conditional arrangement of cells in a mxn matrix unique?

    How many ways to arrange cells of k possible values in a mxn matrix provided that sums of all rows and columns are known? For example, if we have a 5x3 matrix and 10 possible values ( from 0 to 9) that can be assigned for each cell, then how many ways to arrange cells in that matrix satisfying...
  45. Fantini

    MHB Relation between matrix elements of momentum and position operators

    Hello. I'm having trouble understanding what is required in the following problem: Find the relation between the matrix elements of the operators $\widehat{p}$ and $\widehat{x}$ in the base of eigenvectors of the Hamiltonian for one particle, that is, $$\widehat{H} = \frac{1}{2M} \widehat{p}^2...
  46. P

    Matrix form of Density Operator

    Hi All, I have spent hours trying to understand the matrix form of Density Operator. But, I fail. Please see page 2 of the attached file. (from the book "Quantum Mechanics - The Theoretical Minimum" page 199). Most appreciated if someone could enlighten me this. Many thanks in advance. Peter Yu
  47. B

    MHB Exploring Hermitian Matrix Properties in Quantum Mechanics

    Hi Folks, I am looking at Shankars Principles of Quantum Mechanics. For Hermitian Matrices M^1, M^2, M^3, M^4 that obey M^iM^j+M^jM^i=2 \delta^{ij}I, i,j=1...4 Show that eigenvalues of M^i are \pm1 Hint: Go to eigenbasis of M^i and use equation i=j. Not sure how to start this? Should I...
  48. B

    MHB Eigenvectors of 2*2 rotation matrix

    Hi Folks, I calculate the eigenvalues of \begin{bmatrix}\cos \theta& \sin \theta \\ - \sin \theta & \cos \theta \end{bmatrix} to be \lambda_1=e^{i \theta} and \lambda_2=e^{-i \theta} for \lambda_1=e^{i \theta}=\cos \theta + i \sin \theta I calculate the eigenvector via A \lambda = \lambda V as...
  49. 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.
  50. Strilanc

    What's the unitary matrix equivalent to a beam splitter?

    I've seen various different matrices used to represent beam splitters, and am wondering which is the "right" one. Alternatively, are there various kinds of beam splitters but everyone just ambiguously calls them the same thing? The matrices I've seen are the...
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