Matrix Definition and 1000 Threads

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. V

    Is it ok to assume matrices A and B as identity matrix?

    Since ##AB = B##, so matrix ##A## is an identity matrix. Similarly, since ##BA = A## so matrix ##B## is an identity matrix. Also, we can say that ##A^2 = AA=IA= A## and ##B^2 = BB=IB= B##. Therefore, ##A^2 + B^2 = A + B## which means (a) is a correct answer. Also we can say that ##A^2 + B^2 =...
  2. M

    Proving inverse of a 2 x 2 matrix is really an inverse

    For this, Dose someone please know how ##ad - bc## and ##-cb + da## are equal to 1? Many thanks!
  3. V

    Transformations to both sides of a matrix equation

    I feel if we have the matrix equation X = AB, where X,A and B are matrices of the same order, then if we apply an elementary row operation to X on LHS, then we must apply the same elementary row operation to the matrix C = AB on the RHS and this makes sense to me. But the book says, that we...
  4. Euge

    POTW Comparing Rank and Trace of a Matrix

    Let ##M## be a nonzero complex ##n\times n##-matrix. Prove $$\operatorname{rank}M \ge |\operatorname{trace} M|^2/\operatorname{trace}(M^\dagger M)$$ What is a necessary and sufficient condition for equality?
  5. M

    Free variables for a matrix in REF

    For this, I am not sure what the '2nd and 5th the variables' are. Dose someone please know whether the free variables ##2, 0, 0## from the second column and ##5, 8, \pi##? Or are there only allowed to be one free variable for each column so ##2## and ##5## for the respective columns. Also...
  6. S

    Is it possible to find matrix A satisfying certain conditions?

    Since Ax = b has no solution, this means rank (A) < m. Since ##A^T y=c## has exactly one solution, this means rank (##A^T##) = m Since rank (A) ##\neq## rank (##A^T##) so matrix A can not exist. Is this valid reasoning? Thanks
  7. S

    Prove there does not exist invertible matrix C satisfying A = CB

    My attempt: Let C = $$\begin{pmatrix} c_{11} & c_{12} & c_{13} \\ c_{21} & c_{22} & c_{23} \\ c_{31} & c_{32} & c_{33} \end{pmatrix}$$ If C is multiplied by B, then: 1) a21 = c21 . b11 0 = c21 . b11 ##\rightarrow c_{21}=0## 2) a31 = c31 . b11 0 = c31 . b11 ##\rightarrow c_{31}=0## 3) a32 =...
  8. S

    Condition such that the symmetric matrix has only positive eigenvalues

    My attempt: $$ \begin{vmatrix} 1-\lambda & b\\ b & a-\lambda \end{vmatrix} =0$$ $$(1-\lambda)(a-\lambda)-b^2=0$$ $$a-\lambda-a\lambda+\lambda^2-b^2=0$$ $$\lambda^2+(-1-a)\lambda +a-b^2=0$$ The value of ##\lambda## will be positive if D < 0, so $$(-1-a)^2-4(a-b^2)<0$$ $$1+2a+a^2-4a+4b^2<0$$...
  9. R

    B Row reduction, Gaussian Elimination on augmented matrix

    Hi! Please, could you help me on how to solve the following matrix ? I need to replace the value 3 on the third line by 0, the first column need to remain zero and 1 for the third column. I'm having a lot of difficulties with this. How would you proceed ? Thank you for your time and help...
  10. richard_andy

    A Relation between the density matrix and the annihilation operator

    This question is related to equation (1),(3), and (4) in the [paper][1] [1]: https://arxiv.org/abs/2002.12252
  11. entropy1

    B How to multiply matrix with row vector?

    How do I calculate a 3x3 matrix multiplication with a 3 column row vector, like below? ## \begin{bmatrix} A11 & A12 & A13\\ A21 & A22 & A23\\ A31 & A32 & A33 \end{bmatrix}\begin{bmatrix} B1 & B2 & B3 \end{bmatrix} ##
  12. C

    3x3 matrix with complex numbers

    The attempt at a solution: I tried the normal method to find the determinant equal to 2j. I ended up with: 2j = -4yj -2xj -2j -x +y then I tried to see if I had to factorize with j so I didn't turn the j^2 into -1 and ended up with 2 different options: 1) 0= y(-4j-j^2) -x(2j-1) -2j 2)...
  13. A

    I About writing a unitary matrix in another way

    It is easy to see that a matrix of the given form is actually an unitary matrix i,e, satisfying AA^*=I with determinant 1. But, how to see that an unitary matrix can be represented in the given way?
  14. E

    I Fundamental matrix of a second order 2x2 system of ODEs

    Let ## \mathbf{x''} = A\mathbf{x} ## be a homogenous second order system of linear differential equations where ## A = \begin{bmatrix} a & b\\ c & d \end{bmatrix} ## and ## \mathbf{x} = \begin{bmatrix} x(t)\\ y(t)) \end{bmatrix} ## Now to solve this equation we transform it into a 4x4...
  15. Umesh

    A How to take a matrix outside the diagonal operator?

    How to derive (proof) the following trace(A*Diag(B*B^T)*A^T) = norm(W,2), where W = vec(sqrt(diag(A^T*A))*B) & sqrt(diag(A^T*A)) is the square root of diag(A^T*A), B & A are matrix. Please see the equation 70 and 71 on page 2068 of the supporting matrial.
  16. R

    A Solve a nonlinear matrix equation

    Hi all, I want to know if a second solution exists for the following math equation: Ce^{At} ρ_p+(CA)^{−1} (e^{At}−I)B=0 Where C, ρ_p, A and B are constant matrices, 't' is scalar variable. I know that atleast one solution i.e. 〖t=θ〗_1 exists, but I want a method to determine if there is...
  17. nomadreid

    I Cycles from patterns in a permutation matrix

    In a permutation matrix (the identity matrix with rows possibly rearranged), it is easy to spot those rows which will indicate a fixed point -- the one on the diagonal -- and to spot the pairs of rows that will indicate a transposition: a pair of ones on a backward diagonal, i.e., where the...
  18. K

    How Can We Prove the Conjugate Transpose Property of Complex Matrices?

    TL;DR Summary: For every Complex matrix proove that: (Y^*) * X = complex conjugate of {(X^*) * Y} Here (Y^*) and (X^*) is equal to complex conjugate of (Y^T) and complex conjugate of (X^T) where T presents transponse of matrix I think we need to use (A*B)^T= (B^T) * (A^T) and Can you help...
  19. S

    I Consistent matrix index notation when dealing with change of basis

    Until now in my studies - matrices were indexed like ##M_{ij}##, where ##i## represents row number and ##j## is the column number. But now I'm studying vectors, dual vectors, contra- and co-variance, change of basis matrices, tensors, etc. - and things are a bit trickier. Let's say I choose to...
  20. P

    A Purification of a Density Matrix

    I'm trying to find the purification of this density matrix $$\rho=\cos^2\theta \ket{0}\bra{0} + \frac{\sin^2\theta}{2} \left(\ket{1}\bra{1} + \ket{2}\bra{2} \right) $$ So I think the state (the purification) we're looking for is such Psi that $$ \ket{\Psi}\bra{\Psi}=\rho $$ But I'm not...
  21. James1238765

    I Evaluating the quark neutrino mixing matrix

    The mixing of the 3 generations of fermions are tabulated into the CKM matrix for quarks: $$ \begin{bmatrix} c_{12}c_{13} & s_{12}c_{13} & s_{13}e^{-i\sigma_{13}} \\ -s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\sigma_{12}} & c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\sigma_{13}} & s_{23}c_{13} \\...
  22. Mayhem

    B Operator that returns unique number of binary matrix

    If we have an arbitrary square matrix populated randomly with 1s and 0s, is there an operator which will return a unique number for each configuration of 1s and 0s in the matrix? i.e. an operation on $$ \begin{pmatrix} 1 &0 &0 \\ 1 & 0 & 1\\ 0 & 1 & 0 \end{pmatrix} $$ would return something...
  23. C

    Spectral decomposition of 4x4 matrix

    ## A = \pmatrix{ -4 & -3 & 3 & 3 \\ -3 & -4 & 3 & 3 \\ -6 & -3 & 5 & 3 \\ -3 & -6 & 3 & 5 } ## over ## \mathbb{R}##. Let ## T_A: \mathbb{R}^4 \to \mathbb{R}^4 ## be defined as ## T_A v = Av ##. Thus, ## T_A ## represents ## A ## in the standard basis, meaning ## [ T_A]_{e} = A ##. I've...
  24. yucheng

    I Partial trace and the reduced density matrix

    From Rand Lectures on Light, we have, in the interaction picture, the equation of motion of the reduced density matrix: $$i \hbar \rho \dot_A (t) = Tr_B[V(t), \rho_{AB}(t)] = \Sigma_b \langle \phi_b | V \rho_{AB} -\rho_{AB} V | \phi_b \rangle = \Sigma_b \phi_b | \langle V \rho_{AB} | \phi_b...
  25. E

    I From Einstein Summation to Matrix Notation: Why?

    I know that if ##\eta_{\alpha'\beta'}=\Lambda^\mu_{\alpha'} \Lambda^\nu_{\beta'} \eta_{\alpha\beta}## then the matrix equation is $$ (\eta) = (\Lambda)^T\eta\Lambda $$ I have painstakingly verified that this is indeed true, but I am not sure why, and what the rules are (e.g. the ##(\eta)## is in...
  26. chwala

    Express the given matrix in the form ##L_1DU_1##

    $$\begin{bmatrix} 4& 3 \\ 6 & -2 & \\ \end{bmatrix}= \begin{bmatrix} 1& 0 \\ a& 1& \\ \end{bmatrix}⋅ \begin{bmatrix} b& c \\ 0& d& \\ \end{bmatrix}$$ ##b=4, ab=6,⇒b=1.5, d=-6.5, c=3## $$\begin{bmatrix} 4& 3 \\ 6 & -2 & \\ \end{bmatrix} = \begin{bmatrix} 1& 0\\ \dfrac{3}{2} & 1 & \\...
  27. T

    I Getting eigenvalues of an arbitrary matrix with programming

    I have learnt about the power iteration for any matrix say A. How it works is that we start with a random compatible vector v0. We define vn+1 as vn+1=( Avn)/|max(Avn)| After an arbitrary large number of iterations vn will slowly converge to the eigenvector associated with the dominant...
  28. A

    I Determining elements of Markov matrix from a known stationary vector

    Hi, For a 2 x 2 matrix ##A## representing a Markov transitional probability, we can compute the stationary vector ##x## from the relation $$Ax=x$$ But can we compute ##A## of the 2x2 matrix if we know the stationary vector ##x##? The matrix has 4 unknowns we should have 4 equations; so for a ##A...
  29. atyy

    I Are we living in the matrix? No.

    David Tong gives an interesting talk about the lattice chiral fermion problem here. https://weblectures.leidenuniv.nl/Mediasite/Channel/ehrenfestcolloquium/watch/5de33fbc14cd4595a6614ca7683bf71e1d Abstract: Are we living in the matrix? No. Obviously not. It's a daft question. But, buried...
  30. J

    Transformation Matrix T in Terms of β1, β2 with Row Reduction Explained

    T(α1), T(α2), T(α3) written in terms of β1, β2: Tα1 =(1,−3) Tα2 =(2,1) Tα3 =(1,0). Then there is row reduction: Therefore, the matrix of T relative to the pair B, B' is I don't understand why the row reduction takes place? Also, how do these steps relate to ## B = S^{-1}AS ##? Thank you.
  31. A

    Prove the identity matrix is unique

    I would appreciate help walking through this. I put solid effort into it, but there's these road blocks and questions that I can't seem to get past. This is homework I've assigned myself because these are nagging questions that are bothering me that I can't figure out. I'm studying purely on my...
  32. dRic2

    I Transform a 2x2 matrix into an anti-symmetric matrix

    Hi, I have a 2x2 hermitian matrix like: $$ A = \begin{bmatrix} a && b \\ -b && -a \end{bmatrix} $$ (b is imaginary to ensure that it is hermitian). I would like to find an orthogonal transformation M that makes A skew-symmetric: $$ \hat A = \begin{bmatrix} 0 && c \\ -c && 0 \end{bmatrix} $$ Is...
  33. V

    Gaussian Elimination of Singular Matrix with partial pivoting

    Part (A): The matrix is a singular matrix because the determinant is 0 with my calculator. Part (B): Once I perform Gauss Elimination with my pivot being 0.6 I arrive at the last row of matrix entries which are just 0's. So would this be why Gauss Elimination for partial pivoting fails for this...
  34. Ashish Somwanshi

    Matrix representation in QM Assignment -- Need some help please

    This screenshot contains the original assignment statement and I need help to solve it. I have also attached my attempt below. I need to know if my matrices were correct and my method and algebra to solve the problem was correct...
  35. Graham87

    Quantum Mechanics - Matrix representations

    I have found J^2 and Jz, but I am not sure how to find Jx and Jy. I’m thinking maybe use J+-=Jx+-iJy ? But I get unclear results. Thanks!
  36. shahbaznihal

    A Computing the Fisher Matrix numerically

    Hi, I have been studying the Fisher matrix to apply in a project. I understand how to compute a fisher matrix when you have a simple model for example which is linear in the model parameters (in that case the derivatives of the model with respect to the parameters are independent of the...
  37. K

    A Matrix representation of a unitary operator, change of basis

    If ##U## is an unitary operator written as the bra ket of two complete basis vectors :##U=\sum_{k}\left|b^{(k)}\right\rangle\left\langle a^{(k)}\right|## ##U^\dagger=\sum_{k}\left|a^{(k)}\right\rangle\left\langle b^{(k)}\right|## And we've a general vector ##|\alpha\rangle## such that...
  38. S

    Can every symmetric matrix be a matrix of inertia?

    Hello, I am often designing math exams for students of engineering. What I ask is the following: Can I choose any real 3x3 symmetric matrix with positive eigenvalues as a realistic matrix of inertia? Possibly, there are secret connections between the off-diagonal elements (if not zero)...
  39. H

    Prove that every unitary matrix is diagonalisable by a unitary matrix

    Let's assume that ##A## is unitary and diagonalisable, so, we have ## \Lambda = C^{-1} A C ## Since, ##\Lambda## is made up of eigenvalues of ##A##, which is unitary, we have ## \Lambda \Lambda^* = \Lambda \bar{\Lambda} = I##. I tried using some, petty, algebra to prove that ##C C* = I## but...
  40. G

    I Diagonal Matrix of Stress-Energy Tensor: Why?

    I came across a statement in《A First Course in General Relativity》:“The only matrix diagonal in all frames is a multiple of the identity：all its diagonal terms are equal.”Why?I don’t remember this conclusion in linear algebra.The preceding part of this sentence is:Viscosity is a force parallel...
  41. A

    I Changing diagonal elements of a matrix

    I have a variance-covariance matrix W with diagonal elements diag(W). I have a vector of weights v. I want to scale W with these weights but only to change the variances and not the covariances. One way would be to make v into a diagonal matrix and (say V) and obtain VW or WV, which changes both...
  42. A

    Is this vector in the image of the matrix?

    Hello! I have this system here $$ \left[ \begin{matrix} -2 & 4 & \\\ 1 & -2 & {} \end{matrix} \right]x +\begin{pmatrix} 2 \\\ y \end{pmatrix}u $$ Now although the problem is for my control theory class,the background is completely math(as is 90% of control theory) Basically what I need to...
  43. B

    C# How close to Gaussian a 2D Matrix percentage is in C#

    Does anyone know a C# class that can return a value (0 - 100 percentage) of How close a perfect gaussian curve an 2D Matrix is? for example, these would all return a 100%:
  44. H

    Find a matrix ##C## such that ##C^{-1} A C## is a diagonal matrix

    I’m really unable to solve those questions which ask to find a nonsingular ##C## such that $$ C^{-1} A C$$ is a digonal matrix. Some people solve it by finding the eigenvalues and then using it to form a diagonal matrix and setting it equal to $$C^{-1} A C$$. Can you please tell me from scratch...
  45. C

    Transition Rate Matrix for 5 Processing Units

    Summary: The transition rate matrix for a problem where there are 5 Processing Units A computer has five processing units (PU’s). The lifetimes of the PU’s are independent and have the Exp(µ) law. When a PU fails, the computer tries to reconfigure itself to work with the remaining PU’s. This...
  46. C

    Transition matrix of a paint ball game

    Summary: Finding the transition matrix of a paint ball game where only 3 probabilities are given. We have the following question: Alice, Tom, and Chloe are competing in paint ball. Alice hits her target 40% of the time, Tom hits his target 25% of the time, and Chloe hits her target 30% of the...
  47. Haorong Wu

    Solutions of first-order matrix differential equations

    Hello, there. I am trying to solve the differential equation, ##[A(t)+B(t) \partial_t]\left | \psi \right >=0 ##. However, ##A(t)## and ##B(t)## can not be simultaneous diagonalized. I do not know is there any method that can apprixmately solve the equation. I suppose I could write the...
  48. topsquark

    MHB Matrix Methods for Difference Problems II

    This is related to a recent (mainly unserious) post I recently made. I did some more work on a similar problem and I'd like to bounce off an idea why this doesn't work. I really am not sure if I'm right so I'd appreciate a comment. I am working with some simple systems of difference...
  49. topsquark

    MHB Matrix Methods for Difference Problems

    I'm looking at ways of solving 2nd order difference equations with non-constant coefficients. I am working on a method to use transformations (ie rewriting the equation in new variables) to change the form of the equation. Such as a_{n + 2} + f(n) a_{n +1} + g(n) a_n = 0 to something like u_{n...
  50. H

    Vectors as geometric objects and vectors as any mathematical objects

    In geometry, a vector ##\vec{X}## in n-dimensions is something like this $$ \vec{X} = \left( x_1, x_2, \cdots, x_n\right)$$ And it follows its own laws of arithmetic. In Linear Analysis, a polynomial ##p(x) = \sum_{I=1}^{n}a_n x^n ##, is a vector, along with all other mathematical objects of...
Back
Top