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. Richie Smash

    Determine matrix for reflection followed by rotation

    Homework Statement Hi good morning to all. The problem at hand states, that the points A (3,0) and B (5,0) are reflected in the mirror line y=x. Determine the images A' and B' of these points. I've done that using the reflection in the line y=x which i know to be \begin{bmatrix} 0 &1 \\ 1 & 0...
  2. J

    Skew-Hermitian or Hermitian Matrix?

    Homework Statement Homework Equations For Hermition: A = transpose of conjugate of A For Skew Hermition A = minus of transpose of conjugate of AThe Attempt at a Solution I think this answer is C. As Tranpose of conjugate of matrix is this matrix. Book answer is D. Am I wrong or is book wrong?
  3. M

    Calculating Eigenvectors for a 3x3 Matrix: Understanding the Process

    Hi, I am trying to find the eigenvectors for the following 3x3 matrix and are having trouble with it. The matrix is (I have a ; since I can't have a space between each column. Sorry): [20 ; -10 ; 0] [-10 ; 30 ; 0] [0 ; 0 ; 40] I’ve already...
  4. S

    How do I represent grid patterns with a dither matrix?

    Homework Statement PROBLEM STATEMENT: "Represent the grid patterns in the figure with a dither matrix." (Figure: https://www.docdroid.net/OMLUX5v/figure.pdf ) ANSWER (FROM MY BOOK): http://www.wolframalpha.com/input/?i=%7B%7B0,2%7D,%7B3,1%7D%7D Homework Equations...
  5. M

    MHB How can we construct the matrix S ?

    Hey! :o At the block deflation it holds for a non-singular Matrix $S$ \begin{equation*}SAS^{-1}=\begin{pmatrix}C & D \\ O & B\end{pmatrix}\end{equation*} where $O$ is the zero matrix. It holds that $\sigma (A)=\sigma(B)\cup \sigma (C)$, where $\sigma (M)$ is the set of all eigenvalues of a...
  6. M

    A Question about the matrix of a pseudoscalar meson

    Hi everyone, I have a question about the ##q_{1}\bar{q_{2}}## to vacuum : $$ \langle 0 |\bar{q_{2}}\gamma_{\mu}\gamma_{5}q_{1}| q_{1}\bar{q_{2}}\rangle$$ That is the first time I try to solve the question like this. How do we calculate the matrix about this question ? Thank you so much!
  7. M

    MHB Calculation of the inverse matrix - Number of operations

    Hey! :o Let A be a regular ($n\times n$)-Matrix, for which the Gauss algorithm is possible. If we choose as the right side $b$ the unit vectors $$e^{(1)}=(1, 0, \ldots , 0)^T, \ldots , e^{(n)}=(0, \ldots , 0, 1 )^T$$ and calculate the corresponding solutions $x^{(1)}, \ldots , x^{(n)}$ then...
  8. M

    MHB The Determinant of a Matrix with n+1 Ones: Is It Always -1, 0, or 1?

    Hey! :o Let $A \in\mathbb{R}^{n\times n}$, $n\geq 3$ be a matrix with $n+1$ elements $1$ and the remaining elements are $0$. I want to show that $\det (A)\in \{-1, 0, 1\}$ and each of these $3$ possible values can occur. Could you give me a hint how we could show that? I got stuck right now...
  9. Y

    MHB Determining Value of a in Matrix A with $\lambda$ = 0

    Hello all, Given the following matrix, \[A=\begin{pmatrix} 2 & 6\\ 1 & a \end{pmatrix}\] and given that \[\lambda =0\] is an eigenvalue of A, I am trying to determine that value of a. What I did, is to create the characteristic polynomial \[(\lambda -2)*(\lambda -a)+6=0\] and given...
  10. Y

    MHB Symmetric and invertible matrix

    Hello all, If A and B are both squared invertible matrices and A is also symmetric and: \[AB^{-1}AA^{T}=I\] Can I say that \[B=A^{3}\] ? In every iteration of the solution, I have multiplied both sides by a different matrix. At first by the inverse of A, then the inverse of the transpose...
  11. I

    A Second derivative of a complex matrix

    Hi all I am trying to reproduce some results from a paper, but I'm not sure how to proceed. I have the following: ##\phi## is a complex matrix and can be decomposed into real and imaginary parts: $$\phi=\frac{\phi_R +i\phi_I}{\sqrt{2}}$$ so that $$\phi^\dagger\phi=\frac{\phi_R^2 +\phi_I^2}{2}$$...
  12. F

    MHB Showing that a matrix is a homomorphism

    Hi! I am currently working on this question about matrices and showing they are homomorphisms. I have done part (i), but on part (ii) I am confused as the matrix is mapping to a - I have never seen this before and I'm not sure how to approach it. I know that usually you would work out the...
  13. lfdahl

    MHB Prove 2x2 Matrix Puzzle: No $S$ Exists for $S^n$

    Prove, that there is no $2 \times 2$ matrix, $S$, such that \[S^n= \begin{pmatrix} 0 & 1\\ 0 & 0 \end{pmatrix}\] for any integer $n \geq 2$.
  14. J

    Load Flow Order of Jacobian Matrix Power System

    I'm studying Newton Raphson Method in Load Flow Studies. Book has defined Jacobian Matrix and it's order as: N + Np - 1 N = Total Number of Buses Np = Number of P-Q Buses But in solved example they've used some other formula. I'm not sure if it's right. Shouldn't order be: N + Np - 1 N = 40 Np...
  15. Pushoam

    Determinant of exponential matrix

    Homework Statement Homework EquationsThe Attempt at a Solution [/B] Det( ## e^A ## ) = ## e^{(trace A)} ## ## trace(A) = trace( SAS^{-1}) = 0 ## as trace is similiarity invariant. Det( ## e^A ## ) = 1 The answer is option (a). Is this correct? But in the question, it is not...
  16. R

    Easy matrix integration question

    Homework Statement This is just the triple integral of an easy matrix problem. I just have no ideas what they got by the time they got to the integral of x. Homework Equations integral[/B]The Attempt at a Solution Somebody please prove me wrong. I got a matrix of constants by the time I got...
  17. L

    MHB Orthonormal Basis times a real Matrix

    Hi! I have an orthonormal basis for vector space $V$, $\{u_1, u_2, ..., u_n\}$. If $(v_1, v_2, ..., v_n) = (u_1, u_2, ... u_n)A$ where $A$ is a real $n\times n$ matrix, how do I prove that $(v_1, v_2, ... v_n)$ is an orthonormal basis if and only if $A$ is an orthogonal matrix? Thanks!
  18. S

    A Eigenvectors and matrix inner product

    Hi, I am trying to prove that the eigevalues, elements, eigenfunctions or/and eigenvectors of a matrix A form a Hilbert space. Can one apply the inner product formula : \begin{equation} \int x(t)\overline y(t) dt \end{equation} on the x and y coordinates of the eigenvectors [x_1,y_1] and...
  19. T

    Finding eigenvector QM 2x2 matrix

    Homework Statement I am having a issue with how my lecture has normalised the energy state in this question. I will post my working and I will print screen his solution to the given question below, we have the same answer but I am unsure to why he has used the ratio method. Q4. a), b), c)...
  20. C

    How to check if a transformation is surjective and injective

    Homework Statement I have attached the question. Translated: Suppose T: R^4 -> R^4 is the image so that: ... Homework Equations So I did this question and my final answers were correct: 1. not surjective 2. not injective. My method of solving this question is completely different than the...
  21. W

    A Is Normalizing a 4x4 Matrix Possible Using Multiple Methods?

    I am trying to normalize 4x4 matrix (g and f are functions): \begin{equation} G=\begin{matrix} (1-g^2) &0& 0& 0&\\ 0& (1+f^2)& (-g^2-f^2)& 0 \\ 0 &(-g^2-f^2)& (1+f^2)& 0 &\\ 0& 0& 0& (1-g^2) \end{matrix} \end{equation} It's a matrix that's in a research paper (which I don't have) which gives...
  22. Pushoam

    What are the easier ways to calculate eigenvalues for a symmetric matrix?

    Homework Statement Homework EquationsThe Attempt at a Solution I solved it by calculating the eigen values by ##| A- \lambda |= 0 ##. This gave me ## \lambda _1 = 6.42, \lambda _2 = 0.387, \lambda_3 = -0.806##. So, the required answer is 42.02 , option (b). Is this correct? The matrix is...
  23. W

    A How spin projector got included in inverse of Matrix?

    The following matrix A is, \begin{equation} A= \begin{bmatrix} a+b-\sigma\cdot p & -x_1 \\ x_2 & a-b-\sigma\cdot p \end{bmatrix} \end{equation} The inversion of matrix A is, \begin{equation} A^{-1}= \frac{\begin{bmatrix} a-b-\sigma\cdot p & x_1 \\ -x_2 & a+b-\sigma\cdot p...
  24. J6204

    Hill Cipher- Potential Cribs for 3x3 Matrix

    Homework Statement I've created code to crack a Hill Cipher (n=3). I'm unsure which cribs to try to crack a specific code. Would anyone mind posting ideas? The crib must be 9 letters in length. Homework EquationsThe Attempt at a Solution
  25. VSayantan

    Trace of the Exponential of a Square Matrix

    Homework Statement Find the trace of a ##4\times 4## matrix ##\mathbb U=exp(\mathbb A)##, where $$\mathbb A = \begin {pmatrix} 0&0&0&{\frac {\pi}{4}}\\ 0&0&{\frac {\pi}{4}}&0\\ 0&{\frac {\pi}{4}}&0&0\\ {\frac {\pi}{4}}&0&0&0 \end {pmatrix}$$ Homework Equations $$e^{(\mathbb A)}=\mathbb P...
  26. S

    I Consequences on a system of ODEs after performing operations

    Hi, I have derived a matrix from a system of ODE, and the matrix looked pretty bad at first. Then recently, I tried the Gauss elimination, followed by the exponential application on the matrix (e^[A]) and after another Gauss elimination, it turned "down" to the Identity matrix. This is awfully...
  27. S

    I Types of complex matrices, why only 3?

    Hi, the three main types of complex matrices are: 1. Hermitian, with only real eigenvalues 2. Skew-Hermitian , with only imaginary eigenvalues 3. Unitary, with only complex conjugates. Shouldn't there be a fourth type: 4. Non-unitary-non-hermitian, with one imaginary value (i.e. 3i) and a...
  28. M

    MHB Solving Transition Matrix: Octopus Training

    Hey! :o An octopus is trained to chosose from two objects A and B always the object A. Repeated training shows the octopus both objects, if the octopus chooses object A, he will be rewarded. The octopus can be in 3 levels of training: Level 1: He can not remember which object was rewarded...
  29. S

    I Is the Frobenius Norm a Reliable Indicator of Matrix Conditioning?

    I have calculated that a matrix has a Frobenius norm of 1.45, however I cannot find any text on the web that states whether this is an ill-posed or well-posed indication. Is there a rule for Frobenius norms that directly relates to well- and ill-posed matrices? Thanks
  30. S

    I Convert complex ODE to matrix form

    Hi, I have the following complex ODE: aY'' + ibY' = 0 and thought that it could be written as: [a, ib; -1, 1] Then the determinant of this matrix would give the form a + ib = 0 Is this correct and logically sound? Thanks!
  31. D

    Algorithm to matrix product MSR format

    Hi everybody, I'm writing some algebra classes in C++ , Now I'm implementing the modified sparse row matrix , I wrote all most all of the class, but I didn't find the way saving computing time to perform the product of two Modified sparse row matrix .. if you don't know it you can read in the...
  32. Wrichik Basu

    B Why does a matrix diagonalise in this case?

    Why does a matrix become diagonal when sandwiched between "change of matrices" whose columns are eigenvectors?
  33. S

    I How to check if a matrix is Hilbert space and unitary?

    I have a matrix, [ a, ib; -1 1] where a and b are constants. I have to represent and analyse this matrix in a Hilbert space: I take the space C^2 of this matrix is Hilbert space. Is it sufficient to generate the inner product: <x,y> = a*ib -1 and obtain the norm by: \begin{equation}...
  34. S

    I How to study an ODE in matrix form in a Hilbert space?

    Hello, I have derived the matrix form of one ODE, and found a complex matrix, whose phase portrait is a spiral source. The matrix indicates further that the ODE has diffeomorphic flow and requires stringent initial conditions. I have thought about including limits for the matrix, however the...
  35. B

    Matrix Exponential Homework: Eigenvalues & Eigenvectors

    Homework Statement Show that if ##λ##and ##V ## are a pair of eigenvalue and eigenvector for matrix A, $$e^Av=e^λv$$ Homework Equations ##e^A=\sum\limits_{n=0}^\infty\frac{1}{n!}A^n## The Attempt at a Solution I don't know where to start.
  36. Drakkith

    Finding the Standard Matrix of a Linear Transformation

    Homework Statement Let ##T:ℝ^3→ℝ^2## be the linear transformation defined by ##\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}\mapsto \begin{bmatrix} x_1 + x_2 + x_3\\ 0 \end{bmatrix}##. i. Find the standard matrix for ##T##. Homework EquationsThe Attempt at a Solution For this problem I was...
  37. M

    Constructing a 3x3 Linear system question

    Homework Statement Construct a 3 × 3 example of a linear system that has 9 different coefficients on the left hand side but rows 2 and 3 become zero in elimination. If the right hand sude of your system is <b1,b2,b3> (Imagine this is a column vector) then how many solutions does your system...
  38. M

    Reducing a matrix to echelon form

    Homework Statement (i) Reduce the system to echelon form C|d (ii) For k = -12, what are the ranks of C and C|d? Find the solution in vector form if the system is consistent. (iii) Repeat part (b) above for k = −18 Homework Equations Gaussian elimination I used here...
  39. S

    I Converting a Single ODE to Matrix Form for Eigenvalue Analysis

    Hi, I have the following ODE: aY'' + bY' + c = 0 I would like to convert it to a matrix, so to evaluate its eigenvalues and eigenvectors. I have done so for phase.plane system before, however there were two ODEs there. In this case, there is only one, so how does this look like in a matrix...
  40. S

    I Can a Hermitian matrix have complex eigenvalues?

    Hi, I have a matrix which gives the same determinant wether it is transposed or not, however, its eigenvalues have complex roots, and there are complex numbers in the matrix elements. Can this matrix be classified as non-Hermitian? If so, is there any other name to classify it, as it is not...
  41. Drakkith

    Showing That the Eigenvalue of a Matrix is 0

    Homework Statement Show that if ##A^2## is the zero matrix, then the only eigenvalue of ##A## is 0. Homework Equations ##Ax=λx##. The Attempt at a Solution For ##A^2## to be the zero matrix it looks like: ##A^2 = AA=A[A_1, A_2, A_3, ...] = [a_{11}a_{11}+a_{12}a_{21}+a_{13}a_{31} + ... = 0...
  42. M

    Finding values to make a linear system consistent

    Homework Statement Given the following matrix: I need to determine the conditions for b1, b2, and b3 to make the system consistent. In addition, I need to check if the system is consistent when: a) b1 = 1, b2 = 1, b3 = 3 b) b1 = 1, b2 = 0., b3 = -1 c) b1 = 1, b2 = 2, b3 = 3 Homework...
  43. M

    Coefficients that make Gaussian elimination impossible?

    Homework Statement Given this matrix: I am asked to find values of the coefficient of the second value of the third row that would make it impossible to proceed and make elimination break down. Homework Equations Gaussian elimination methods I used given here...
  44. S

    I How can I analyse and classify a matrix?

    Hi, I have a matrix of an ODE which yields complex eigenvalues and eigenvectors. It is therefore not Hermitian. How can I further analyse the properties of the matrix in a Hilbert space? The idea is to reveal the properties of stability and instability of the matrix. D_2 and D_1 are the second...
  45. Drakkith

    Showing that S is an Eigenvalue of a Matrix

    Homework Statement Consider an n x n matrix A with the property that the row sums all equal the same number S. Show that S is an eigenvalue of A. [Hint: Find an eigenvector.] Homework Equations ##Ax=λx## The Attempt at a Solution S is just lambda here, so I begin solving this just like you...
  46. Drakkith

    Finding the Eigenvalue of a Matrix

    Homework Statement Find the eigenvalues of the matrix ##\begin{bmatrix} 4 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & 0 & -3 \end{bmatrix}## Homework Equations ##Ax=λx## The Attempt at a Solution I'm having some trouble finding the eigenvalues of this matrix. The eigenvalue of a matrix is a scalar λ such...
  47. R

    Using Kirchoff's Voltage Rule to find currents in a system

    Homework Statement Then solve these equations for i1-4 Homework Equations V=IR The Attempt at a Solution 80i_1-50i_2-30i_3 = -120 -50i_1+100i_2-10i_3-25i_4 = 0. -30i_1-10i_2+65i_3-20i_4 = 0. -25i_2-20i_3+100i_4 = 0. i_1=-4.18239492 i_2=-2.66455194 i_3=-2.71213323 i_4=-1.20856463...
  48. Drakkith

    Does the Null Space of a 2x3 Matrix Determine its Column Space?

    Homework Statement Let ##A## be a 2x3 matrix. If Nul(##A##) is a line through the origin in ℝ3, then Col(##A##) = ℝ2. Explain why. Hint: Think about the number of pivots in ##A##. Homework EquationsThe Attempt at a Solution So, Nul(##A##) is the set of all solutions to the equation ##Ax=0##...
  49. Ron Burgundypants

    Eigenvalues and vectors of a 4 by 4 matrix

    Homework Statement Coupled Harmonic Oscillators. In this series of exercises you are asked to generalize the material on harmonic oscillators in Section 6.2 to the case where the oscillators are coupled. Suppose there are two masses m1 and m2 attached to springs and walls as shown in Figure...
  50. R

    Coupled differential equations using matrix exponent

    Homework Statement Solve the following coupled differential equations by finding the eigenvectors and eigenvalues of the matrix and using it to calculate the matrix exponent: $$\frac{df}{dz}=i\delta f(z)+i\kappa b(z)$$ $$\frac{db}{dz}=-i\delta b(z)-i\kappa f(z)$$ In matrix form...
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