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.

View More On Wikipedia.org
Recent contents Top users
  1. Z

    Exponential of hermitian matrix

    Homework Statement Let A be a Hermitian matrix and consider the matrix U = exp[-iA] defined by thr Taylor expansion of the exponential. a) Show that the eigenvectors of A are eigenvectors of U. If the eigenvalues of A are a subscript(i) for i=1,...N, show that the eigenvalues of U are...
  2. X

    Finding Matrix B from given info

    Homework Statement Use the given info to find matrix B Homework Equations (I + 3B)^-1 = [5 2; 4 2] to make more clear: inv(I + 3B) = this 2x2 matrix: top row = 5 2, bottom row = 4 2 The Attempt at a Solution I tried multiplying both sides of the eqn by I + 3B to get I = [5 2; 4...
  3. S

    I How can I find the orthogonal matrix that diagonalises a given matrix?

    I want to find the orthogonal matrix ##\begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}## which diagonalises the matrix ##\begin{pmatrix} 0 & m\\ m & M \end{pmatrix}##. The eigenvalues are easily found to be ##\lambda = \frac{M}{2} \pm...
  4. A

    Choose h and k so that the matrix has a unique solution

    Homework Statement $$ A = \begin{bmatrix} 1 & 2\\ 2 & h\\ = k \end{bmatrix} $$ Mod note: Corrected augmented matrix: ##\begin{bmatrix} 1 & 2 & | & 2 \\ 2 & h & | & k \end{bmatrix}## Homework EquationsThe Attempt at a Solution Ok, so apparently it's a bad idea to...
  5. Zero2Infinity

    Write a matrix given the null space

    Homework Statement Build the matrix A associated with a linear transformation ƒ:ℝ3→ℝ3 that has the line x-4y=z=0 as its kernel. Homework Equations I don't see any relevant equation to be specified here . The Attempt at a Solution First of all, I tried to find a basis for the null space by...
  6. M

    Determinant of Matrix Component

    Homework Statement Show $$\frac{\partial \det(A)}{\partial A_{pq}} = \frac{1}{2}\epsilon_{pjk}\epsilon_{qmn}A_{jm}A_{kn}$$ Homework Equations ##\det(A)=\epsilon_{ijk}A_{1i}A_{2j}A_{3k}## The Attempt at a Solution $$\frac{\partial \det(A)}{\partial A_{pq}}=\frac{\partial}{\partial...
  7. J

    Confusion with how to make an augmented matrix

    Homework Statement So in the attachment you'll see a picture taken from a linear algebra book where a linear system of equations is presented in the equivalent augmented matrix form. I'm confused about the representation of the first equation in the augmented matrix. What happened to the...
  8. TeethWhitener

    I Is a symmetric matrix with positive eigenvalues always real?

    I split off this question from the thread here: https://www.physicsforums.com/threads/error-in-landau-lifshitz-mechanics.901356/ In that thread, I was told that a symmetric matrix ##\mathbf{A}## with real positive definite eigenvalues ##\{\lambda_i\} \in \mathbb{R}^+## is always real. I feel...
  9. C

    Question about inverse of matrix

    Homework Statement [/B] Given this matrix ##\begin{bmatrix}As+B \\ C \end{bmatrix}## which is invertible and ##A## has full row rank. I would like to show that its inverse has no terms with ##s## or higher degree if ##\begin{bmatrix}A \\ C \end{bmatrix}## is invertible. Homework Equations...
  10. T

    I Is the trace of a matrix independent of basis?

    Hello, Just wondering if the trace of a matrix is independent of basis, seeing as the trace of a matrix is equal to the sun of the eigenvalues of the operator that the matrix is a representation of. Thank you
  11. G

    A Period matrix of the Jacobian variety of a curve

    Consider an algebraic variety, X which is a smooth algebraic manifold specified as the zero set of a known polynomial. I would appreciate resource recommendations preferably or an outline of approaches as to how one can compute the period matrix of X, or more precisely, of the Jacobian variety...
  12. 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...
  13. V

    I Linear algebra ( symmetric matrix)

    I am currently brushing on my linear algebra skills when i read this For any Matrix A 1)A*At is symmetric , where At is A transpose ( sorry I tried using the super script option given in the editor and i couldn't figure it out ) 2)(A + At)/2 is symmetric Now my question is , why should it be...
  14. Y

    MHB Solving for Invertible Matrix: What Am I Doing Wrong?

    Hello all again, A is a matrix with order nXn, such that: \[A^{3}-2A^{2}+I=0\] I need to choose the correct answer: 1) A is not invertible 2) It is not possible to say if A is invertible 3) \[(A^{-1})^{2}=2I-A\] 4) \[A^{-1}=2I-A\] I can't find the solution here. I tried my own, and got...
  15. Y

    MHB Diagonalizable Matrix: How to Approach?

    Hello all I have this matrix: \[\begin{pmatrix} 6 & 0\\ -3 & a \end{pmatrix}\] And I am told it is diagonalizable. Therefore, the value of a is: 1) a=0 2) a not= 0 3) a not=6 4) a=6 5) a not=0,6 How should I approach this? Is there a "trick" or should I find eigenvalues and eigenvectors for...
  16. M

    MHB What am I misunderstanding?

    Hello! I don't know exactly how to state my question so I'll show you what my problem is. Ex. Let T : R[x]_3 →R be the function defined by T(p(x)) = p(−1) + \int_{0}^{1} p(x) \,dx , where R[x]_3 is a vector space of polynomials with degree at most 3. Show that $T$ is a linear map; write down...
  17. T

    B Matrix exponential and applying it a random state

    Let K be any Matrix, not necessarily the hamitonian. Is $$e^{-Kt}\left|\psi\right>$$ equal to $$e^{-K\left|\psi\right>t}$$ even if it is not the the eigenvector of K? I think so as i just taylor expand the $$e^{-Kt}$$ out but I want to confirm. In that case can i say that...
  18. stevendaryl

    I On uniqueness of density matrix description as mixed state

    If you have a density matrix \rho, there is a basis |\psi_j\rangle such that \rho is diagonal in that basis. What are the conditions on \rho such that the basis that diagonalizes it is unique? It's easy enough to work out the answer in the simplest case, of a two-dimensional basis: Then \rho...
  19. I

    Determining the rank of a matrix

    Homework Statement Homework Equations N/A The Attempt at a Solution I know that they got a rank of 2 since there are 2 linearly independent columns but what if we decided to count rows? In that case we would have 4 linearly independent rows which would suggest the rank is 4? How do we...
  20. A

    I Can we retrieve the inverse of matrix A in this example?

    Suppose we have a product formed by a multiplication of a unitary matrix U and a diagonal matrix A, can we retrieve the inverse of A without knowing either U or A?
  21. Xico Sim

    A Matrix Lie groups and its Lie Algebra

    Hi! I'm studying Lie Algebras and Lie Groups. I'm using Brian Hall's book, which focuses on matrix lie groups for a start, and I'm loving it. However, I'm really having a hard time connecting what he does with what physicists do (which I never really understood)... Here goes one of my questions...
  22. C

    I Towards a matrix element definition of PDF

    In Schwartz's book, 'Quantum Field Theory and the Standard Model' P.696, he starts to derive an expression for a parton distribution function in terms of matrix elements evaluated on the lightcone. Most of the derivation is clear to me, except a couple of things at the start and midway. The...
  23. mnb96

    Question about capacitance matrix

    Hello, suppose I have four conductors (1,2,3,4) and I know their mutual capacitances cij where i,j∈{1,2,3,4}. Note that the quantities cij are essentially the elements of the capacitance matrix of this system. Now, if I apply a voltage to two conductors and leave the other two grounded (e.g...
  24. Z

    MHB How to find the Domain , Range , matrix for the relation R

    can anyone help me ? i have a homework and i did't find any answer for it the question is find the Domain , Range , matrix and the digraph for the relation R a ) A = { 1,2,3,4,8 } = B , aRb if and only if a=b b) A = { 1,2,3,4,6 } =B , aRb if and only if a multiple of b
  25. M

    MHB Why does this hold when we have the zero matrix?

    Hey! :o I want to show that for $A,B\in \mathbb{R}^{2\times 2}$ the $U=\{X\in \mathbb{R}^{2\times 2}\mid AX=XB\}$ is a vector subspace of $\mathbb{R}^{2\times 2}$. We have that it is non-empty, since the zero matrix belongs to $U$ : $AO=O=OB$. Let $X_1, X_2\in U$ then $AX_1=X_1B$ and...
  26. A

    MHB How to Quickly Find the Rank of a 4 x 6 Matrix Using Column Operations

    Is there any shortcut to find the rank of this $4 \times 6$ matrix quickly? $$A = \begin{pmatrix} -3 &2 &-1 &-2 &7 &-1\\ 9 &2 &27 &18 &7 &-9\\ 3 &2 &1 &0 &7 &-1\\ 6 &2 &8 &4 &-7 &-4\\ \end{pmatrix}$$ The above is a sample question for semester final test. If it were a homework, of course I...
  27. Mr Davis 97

    T/F: Whether a matrix is diagonalizable

    Homework Statement T/F: The matrix ##\begin{bmatrix} 2 & 1 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}## is diagonalizable. Homework EquationsThe Attempt at a Solution Is there a quick way to tell whether the matrix is diagonalizable? Since it's a T/F question, that would seem to...
  28. Mr Davis 97

    Matrix A and its inverse have the same eigenvectors

    Homework Statement T/F: Each eigenvector of an invertible matrix A is also an eignevector of A-1 Homework EquationsThe Attempt at a Solution I know that if A is invertible and ##A\vec{v} = \lambda \vec{v}##, then ##A^{-1} \vec{v} = \frac{1}{\lambda} \vec{v}##, which seems to imply that A and...
  29. A

    Setting Up a Matrix with Order Unity Elements: A Scientist's Guide

    Homework Statement A determinant with all elements of order unity may be surprisingly small. The Gilbert determinant Hij=(I+j-1)^-1, i,j=2... n is notorious for its small values. Homework EquationsThe Attempt at a Solution I just need help setting up the matrix and I can solve it myself. Thanks
  30. W

    Python Adding Matrix with Variables in Jupyter Notebook

    i All, I have a Jupyter Python Notebook with data like below: \ I want to create an SFrame with 2 columns and 11 rows.Each row has two entries: One containing the name of each word and the other entry containing the total count of the word. The words are part of a list called 'Selected...
  31. JulienB

    Interpreting a system matrix (optics)

    Homework Statement Hi everybody! While doing some homework for school, I realized that I still struggle to get what are the elements of an optical system matrix referring to. Here is the problem: An optical tube with length ##L=50##cm has at one end a convex lens (##D=2##) and at the other...
  32. ShayanJ

    A Entanglement and density matrix in QFTs

    I'm reading this paper. But I haven't read anything on how to calculate the density operator in a QFT or how to calculate its trace. Now I can't follow this part of the paper. Can anyone clarify? Thanks
  33. S

    Numerical implementation of a matrix derivative

    Homework Statement Hi all! I'm having trouble understanding the implementation of some derivatives in the expression (1) of this article: https://www.ncbi.nlm.nih.gov/pubmed/26248210 How do I implement ∑(ij) ∂ijw ? Thank you all in advance. Homework Equations w is a square matrix(120x120)...
  34. Dishsoap

    Density matrix of spin 1 system

    Homework Statement Consider an ensemble of spin 1 systems (a mixed state made of the spin 1 system). The density matrix is now a 3x3 matrix. How many independent parameters are needed to characterize the density matrix? What must we know in addition to Sx, Sy and Sz to characterize the mixed...
  35. Math Amateur

    I Introduction to Simple Matrix Rings in Noncommutative Algebra

    I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of Bresar's Example 1.10 on a simple matrix ring over a division ring ... Example 1.10, including some...
  36. Math Amateur

    MHB Understanding Bresar's Example 1.10 on Simple Matrix Rings: Can Anyone Help?

    I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of Bresar's Example 1.10 on a simple matrix ring over a division ring ... Example 1.10...
  37. M

    MHB How should this matrix be multiplied

    $A=\begin{bmatrix} 3&2\\ \end{bmatrix} B=\begin{bmatrix} 1\\ 2\end{bmatrix}$ Find the value of the matrix $AB$. The order of the first matrix is 1*2 The order of the second matrix is 2*1 Matrix AB should be 1*1 I am a bit struggling in determining the way...
  38. A

    Find an appropriate matrix according to specific conditions

    I am facing some difficulties solving one of the questions we had in our previous exam. I am sorry for the bad translation , I hope this is clear. In each section, find all approppriate matrices 2x2 (if exists) , which implementing the given conditions: is an eigenvector of A with eigenvalue...
  39. M

    How to interpret a complex Matrix as a Probability Matrix?

    Hello everyone, I'have implemented a Maximum-Likelihood-Expectation-Maximization Algorithm in order to reconstruct a bild. let say, we have such a system Ax=b, where A is a complex matrix, b is a complex vector. A and b are known and we will iterately try to find the best x (which should be...
  40. 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...
  41. J

    A Efficiently Computing Eigenvalues of a Sparse Banded Matrix

    I have a Hamiltonian represented by a penta-diagonal matrix The first bands are directly adjascent to the diagonals. The other two bands are N places above and below the diagonal. Can anyone recommend an efficient algorithm or routine for finding the eigenvalues and eigenvectors?
  42. 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...
  43. M

    MHB Proving Idempotency of a Matrix: A Step-by-Step Guide

    Hey! :o We have that a matrix $A$ is idempotent if it holds that $A^2=A$. We suppose that $X$ is a $m\times n$-matrix and that $(X^TX)^{-1}$ exists. I want to show that $A=I_m-X(X^TX)^{-1}X^T$ is idempotent. I have done the following: $$A^2 =A\cdot A=(I_m-X(X^TX)^{-1}X^T)\cdot...
  44. Konte

    I Hamiltonian matrix - Eigenvectors

    Hello everybody, From a complete set of orthogonal basis vector ##|i\rangle## ##\in## Hilbert space (##i## = ##1## to ##n##), I construct and obtain a nondiagonal Hamiltonian matrix $$ \left( \begin{array}{cccccc} \langle1|H|1\rangle & \langle1|H|2\rangle & . &. &.& \langle1|H|n\rangle \\...
  45. Kernul

    Solution of system with matrix

    Homework Statement Find out for which values of ##\alpha## the system ##AX + \alpha X = (1, 1, 1, 1)^t## has solutions. $$A = \begin{pmatrix} 6 & 0 & -1 & 2 \\ 3 & 5 & -3 & 6 \\ -2 & 0 & 7 & -4 \\ 2 & 0 & 1 & 0 \end{pmatrix} X = \begin{pmatrix} x \\ y \\ z \\ t \end{pmatrix}$$ Homework...
  46. I

    I From Non Hermitian to Hermitian Matrix

    Is there any way that i can convert a non-hermitian matrix to a hermitian matrix ?
  47. I

    Inertia matrix of a homogeneous cylinder

    Homework Statement [/B] Homework Equations N/A The Attempt at a Solution What I am confused about is where they got the (1/4)mR^2 + (1/12)ml^2 and (1/2)mR^2 from? I am guessing that these came from the integral of y'^2 + z'^2 and x'^2 +y'^2 but I don't understand how this happened exactly...
  48. R

    Finding transition matrix, no % probability given

    Homework Statement Consider a quantum mechanical system with three states. At each step a particular particle transitions from one state to a different state. Empirical data show that if the particle is in State 1, then it is 7 times more likely to go to State 2 at the next step than to State...
  49. R

    Stuck finding a specific value of an inverse of a complex matrix

    Homework Statement Consider the following matrix. A = 2 + 4i...1 + 5i 2 − 3i...2 + 3i Let B = A-1. Find b12 (i.e., find the entry in row 1, column 2 of A−1) Homework Equations A-1 = 1/(ad - cb)* [ d -b ] [ -c a ] <--imagine as 2x2 matrix with first row (d,-b) and second row...
  50. A

    Calculators How to insert a matrix from a website into a sheet?

    Say, I have a matrix which I obtained from a website for matrix calculation, how to insert it into an excel so as for each cell in the matrix, there is a corresponding cell in the excel sheet?
Back
Top