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. Abhishek11235

    A How to calculate the matrix of a form?

    This is screenshot from V.I Arnold's book on Classical mechanics. My question is how do we find matrix of any n-form. Detailed answer please.
  2. EEristavi

    Solving a System of Equations via the Matrix Method

    I have equation system: x + y + z - a*k = 0 -b*x + y + z = 0 -c*y + z = 0 -d*x + y = 0 where: a, b, c, d = const. Have to find: x, y, z, k Attempt of solution: I create Matrix A with coefficients; Matrix B - Solutions (Zeros) and Matrix X - variables. When I try to use Cramer's rule -...
  3. cookiemnstr510510

    Solving Linear Algebra Problem 8: Gauss-Jordan Method

    Hello All, I have a question regarding the wording of this problem and my method of solving. (Problem and directions attached in Linear.jpg) PROBLEM 8 NOT 7! :) Here is my thought process: Keep doing elementary row operations until we have it it gauss-jordan form, then we have our answers?! I...
  4. cookiemnstr510510

    I How to Write a Matrix on a Webpage?

    Hello, sorry if this is in the incorrect thread but I am wondering how I write a matrix on here? Much help appreciated and more problems to come ;) Thanks!
  5. V

    Solve Matrix A: Homework Equations & Solution

    Homework Statement Solve for the Matrix A. (AT + 4I)-1 = [-1 1, 2 1] Homework EquationsThe Attempt at a Solution I am unsure of how exactly to do this. Here is what I have done: (A-1)T = 1/4I + [-1 1, 2 1] Am I on track? Thank you.
  6. M

    MHB The decomposition for a symmetric positiv definite matrix is unique

    Hey! :o We have the matrix \begin{equation*}A=\begin{pmatrix}1/2 & 1/5 & 1/10 & 1/17 \\ 1/5 & 1/2 & 1/5 & 1/10 \\ 1/10 & 1/5 & 1/2 & 1/5 \\ 1/17 & 1/10 & 1/5 & 1/10\end{pmatrix}\end{equation*} I have applied the Cholesky decomposition and found that $A=\tilde{L}\cdot \tilde{L}^T$ where...
  7. Mutatis

    Find the eigenvalues and eigenvectors

    Homework Statement Find the eigenvalues and eigenvectors of the following matrix: $$ A = \begin{bmatrix} 3 & 0 & 0 \\ 0 & 3 & 2 \\ 0 & -1 & 0 \end{bmatrix} $$ Homework Equations Characteristic polynomial: $$ \Delta (t) = t^3 - Tr(A) t^2 + (A_{11}+A_{22} +A_{33})t - det(A) .$$ The Attempt at...
  8. S

    I Can't understand a step in an LU decomposition proof

    I'm reading about the LU decomposition on this page and cannot understand one of the final steps in the proof to the following: ---------------- Let ##A## be a ##K\times K## matrix. Then, there exists a permutation matrix ##P## such that ##PA## has an LU decomposition: $$PA=LU$$ where ##L## is a...
  9. karush

    MHB Matrix Addition: OK - No Examples Found

    OK from the text bk I did not see any example of this the circle red is mine ... why is this here so not sure how these questions are to be answered. Much Mahalo
  10. T

    MHB A and solution are known find B matrix

    I have the matrix of A 1 2 -1 2 -1 1 and i am asked if there is any B matrix that can make AB = 1-1 1 1 I assume that this is not possible because if we follow the law of Ax=B then {A}^{-1} * B =x and...
  11. yecko

    One-factor-at-a-time test matrix

    Homework Statement If Z(X,Y) = (X^2+Y^2)*(P(X) + Q(Y)), how to convert it to one-factor-at-a-time test matrix ? Write down the relevant formula and give a brief explanation. Homework Equations below: in my attempt The Attempt at a Solution Z(X1,X4) =P(X1)*Q(X4)...
  12. F

    I Fisher matrix - equivalence or not between sequences

    I am currently studying Fisher's formalism as part of parameter estimation. From this documentation : They that Fisher matrix is the inverse matrix of the covariance matrix. Initially, one builds a matrix "full" that takes into account all the parameters. 1) Projection : We can then do...
  13. karush

    MHB Find $(AB)^T$: Calculate Matrix Product & Transpose

    Let $A=\left[\begin{array}{c}1 & 2 & -3 \\ 2 & 0 & -1 \end{array}\right] \textit { and } B=\left[\begin{array}{c}3&2 \\ 1 & -1 \\ 0 & 2 \end{array}\right]$ Find $(AB)^T$$AB=\left[ \begin{array}{cc}(1\cdot 3)+(2\cdot1)+(-3\cdot0) & (1\cdot2)+(2\cdot-1)+(-3\cdot2) \\ (2\cdot3)+(0\cdot1)+...
  14. N

    A Particle swarm optimization for matrix inversion

    Hi everyone, I am working on matrix inversion and focusing on low-complexity method such as iterative method. Recently, I am interested to explore how particle swarm optimization (PSO) can be applied to do matrix inversion. Since I am very very new in PSO, I have no idea how to start my work...
  15. F

    Deriving the Matrix for a 3 dimensional rotation

    Homework Statement [/B] The problem consists of deriving the matrix for a 3 dimensional rotation. My approach consisted of constructing an arbitrary vector and rewriting this vector in terms of its magnitude and the angles which define it. Then I increased the angles by some amount each. I...
  16. sarumman

    Proving or Disproving Null Space Containment in F(n) for A and A^2

    Homework Statement given I am required to proove or disprove:[/B] Homework Equations rank dim null space The Attempt at a Solution I tried to base my answer based on the fact that null A and null A^2 is Contained in F (n) and dim N(A)+rank(A)=N same goes for A^2.
  17. N

    Doubting Logic: Boolean Matrix Homework Help

    Homework Statement Homework EquationsThe Attempt at a Solution Does my logic seem right, I'm doubtin my anwsers.
  18. mvgmonteiro

    Maximum determinant of matrix with only 1 and -1 elements?

    1. The problem statement: Find out the maximum determinant of a matrix nxn which have just 1 and -1 elements. 2. The attempt at a solution: I have tried for 2x2 and 3x3 matrices and so generalizing for nxn matrices. But I can’t figure out any pattern or something like that. Also, I barely know...
  19. Morbidly_Green

    Expressing the density matrix in matrix form

    Homework Statement Given the above lambda system, is it wrong to say that the density matrix is of the form ## \rho = c_1|1> + c_2|2> + c_3|3> ## ? Hence when written in matrix form (basis of ##|i>##), ## \rho ## is a diagonal matrix who's elements are the ##c_i##s?
  20. M

    Exporting a matrix to Microsoft Access: Error using database/

    Hello! Below is the code for the following task: matrix "Q" with a dimension of 3*2 was obtained using a matrix of cells "A"; then the matrix "Q" is exported to Microsoft Access with the same dimension (3 rows, 2 columns). (!) The difficulty is that only the first row of the matrix is written...
  21. C

    I Writing Metric in Matrix Form: Method?

    In ##c=1## units, from my SR courses I was told for example, that the Minkowski metric ## ds^2 = -dt^2 + dx^2 + dy^2 + dz^2 ## can be written in matrix form as the below.. \eta = \begin{pmatrix} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} And it was just...
  22. LesterTU

    Expressing Covariant Derivative in Matrix Form

    Homework Statement We are given a Lorentz four-vector in "isospin space" with three components ##\vec v^{\mu} = (v^{\mu}_1, v^{\mu}_2, v^{\mu}_3)## and want to express the covariant derivative $$D^{\mu} = {\partial}^{\mu} - ig\frac {\vec \tau} {2}\cdot \vec v^{\mu}$$ explicitly in ##2\times 2##...
  23. K

    B Number of independent entries of a matrix

    Is there an easy way to figure out the number of independent parameters a given matrix has? For example, a general, real, n x n matrix has n^2 entries and that's easy to realize cause we have a squared array of real numbers. What if this matrix is orthogonal?
  24. M

    MHB Show that the tridiagonal matrix is positive definite

    Hey! :o We have the tridiagonal matrix $A=\begin{pmatrix}2 & 1 & \ldots & 0 \\ 1 & 2 & 1 & \ldots \\ \ldots & \ldots & \ldots & \ldots \\ 0 & \ldots & 1 & 2\end{pmatrix}$. I want to show that it is positive definite. For that it is given the following hint: 1) $\langle x, Ax\rangle \geq 0$...
  25. B

    Engineering Competency matrix for a power engineer?

    What competency matrix are suggested for power consultant engineers? My work organization has a competency matrix of different skills. The skills included different software packages and engineering practices for low/medium/high voltage power design and instrument and controls. Some of the...
  26. CMJ96

    Decomposing a 4x4 unitary matrix

    Homework Statement I want to decompose the following matrix into a product of two level matrices ##V_i## $$ \begin{bmatrix} 0 & 0 & 1 & 0 \\ 0 & \frac{-\sqrt{3}}{2} & 0 & \frac{-1}{2} \\ \frac{\sqrt{3}}{2} & \frac{-1}{4} & 0 & \frac{\sqrt{3}}{4} \\ \frac{1}{2} & \frac{\sqrt{3}}{4} & 0 &...
  27. MattIverson

    Finding the Lagrangian Matrix for Two-Spring Systems

    Homework Statement The problem is attached. I'm working on the second system with the masses on a linear spring (not the first system). I think I solved part (a), but I'm not sure if I did what it was asking for. I'm not sure exactly what the question means by the... L=.5Tnn-.5Vnn. Namely, I'm...
  28. J

    I Density Matrix Quantum Mechanics Help - Hi, I'm Confirming!

    Hi, I am wanting to confirm my understanding of the density matrix in quantum mechanics. Is it the wave function co-efficients squared - in other words the wave amplitudes squared which in turn are the probabilities and then these turn out to be placed into a matrix form with the squared wave...
  29. DuckAmuck

    I Can any matrix be expressed as the product of two vectors?

    For example, does this always hold true? M_ab = v_a × w_b If not, where does it break down?
  30. G

    Adjugate of singular skew-symmetric matrix

    <Moderator's note: Moved from a mathematical forum.> When one differentiates the determinant of a matrix, the adjugate of the matrix comes into play. The formula holds irrespective of whether or not the determinant vanishes. I tried this for the 4x4 electromagnetic field tensor ##F##. But...
  31. D

    I Index placement -- Lorentz transformation matrix

    Hi. I came across the following statement , which seems wrong to me. Λμρ = ( ΛT )ρμ I have it on good authority (a previous post on this forum) that (ΛT)μν = Λνμ so I am hoping that the first equation is wrong ? It looks like the inverse not the transpose ? The equation Λμρ η μνΛνσ = ηρσ is...
  32. F

    Show that a matrix is a Lorentz transformation

    Homework Statement Given the matrix $$ \Omega = \begin{pmatrix} 0 & -\psi & 0 & 0 \\ -\psi & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix}$$ show that ## e^{\Omega}## is a Lorentz transformation along the x-axis with ## \beta = tanh(\psi)## Homework Equations During the lesson we...
  33. Robin04

    I Projection Matrix: Expressing Operator with Vectors

    If we express the projection operator with vectors, we get ##\hat{P}\vec{v} = \vec{e}(\vec{e}\vec{v})## which means that we project ##\vec{v}## onto ##\vec{e}##. We can write this as ##\hat{P}\vec{v} = e_k \sum_{l} e_lv_l = \sum_l (e_ke_l )v_l##. In my class we said that the matrix for the...
  34. C

    MHB Proving matrix group under addition for associative axiom

    Dear Everyone, I have some feeling some uncertainty proving one of the axioms for a group. Here is the proof to show this is a group: Let the set T be defined as a set of 2x2 square matrices with coefficients of integral values and all the entries are the same. We want to show that T is an...
  35. ohwilleke

    I How credible are CKM matrix limits on new physics?

    A pre-print of a conference paper from eleven months ago analyzes the extent to which the available data on the CKM matrix element values rules out beyond the Standard Model Physics. It finds that in the most rigid model dependent analysis, that new physics are excluded up to a characteristic...
  36. S

    How do I get the solution with the matrix exponential method

    Homework Statement a = [1 1;4 1] Homework Equations R = M^-1 * a * M X = M * e^(R*t) * M^-1 * x M is matrix of eigenvectors. The Attempt at a Solution lambda = 3, -1 initial conditions: x = [1 1]' at t = .1 eigenvectors: k1 = [1 2]' k2 = [1 -2]' M = [1 1;2 -2] M^-1 = [.5 .25...
  37. Z

    How to find first matrix of SVD?

    Homework Statement I don't know how to find the first matrix of SVD. I know how to find the middle one and the last one. For first one some tutorials found AV1. I don't know how to find it. Is there any simple way to find the first matrix. 2. Homework Equations [/B] SVD = A*Summation matrix *...
  38. S

    I Further S matrix clarifications

    Hello! I attached a SS of the part of my book that I am confused about. So there they write the initial and final states in term of creation and annihilation operators, acting on the (not free) vacuum i.e. ##|\Omega>##. So first thing, the value of the creation (annihilation) operators at...
  39. S

    I Why do we assume particles are free at infinity in the S matrix theory?

    Hello! I am reading about the S matrix, and I see that one of the assumption that the derivations are based on is the fact that interacting particles are free at ##t=\pm \infty## and I am not sure I understand why. One of the given examples is the ##\phi^4## theory which contains an interaction...
  40. Z

    Calculating Eigenvectors: 3*3 w/o Augmented Matrix

    Homework Statement I am continuing from : https://www.physicsforums.com/threads/finding-eigen-values-list-of-possible-solutions-for-lambda.955164/ I have got a 3 * 3 matrix. I have to find itseigen values and eigen vectors. I have found the eigen values.For calculating eigen vectors they are...
  41. Z

    Problem with calculating eigen vector for 2*2 Matrix

    Homework Statement r1= 2 7 r2=-1 -6 Homework Equations A-lambda*I=0 (A-lambda*I)*x=0 The Attempt at a Solution I have got following eigen values: lambda1 = -5 and lambda2=1 A-lambdaI matrix is: r1 = 7 7 r2 = -1 -1 and x matrix is: r1 =x r2 =y I can't understand why we have to use...
  42. Sanchayan Ghosh

    I Canonical form derivation of (L1'AL1)

    Hello everyone, I actually had a problem with understanding the part where they have defined L'AL = Λ. There, they have taken γΛγ1 = Σy2λ = 1. Why have they taken that? Is it arbitary or does it come as a result of a derivation? Thank you
  43. Z

    How Do You Find Eigenvectors of a 2x2 Matrix?

    Homework Statement Consider the following Matrix: Row1 = 2 2 Row2 = 5 -1 Find its Eigen Vectors Homework Equations Ax = λx & det(A − λI)= 0. The Attempt at a Solution First find the det(A − λI)= 0. which gives a quadratic eq. roots are λ1 = -3 and λ2 = 4 (Eigen values) Then using λ1, I...
  44. S

    Are Similar Matrices' Eigenvalues the Same? Solving for Symmetric Matrices

    Homework Statement Consider matrices A = [1 2;2 4] and P = [1 3;3 6]. Using B = P^-1*A*P, verify that similar matrices have the same eigenvalues. Find the eigenvectors y for B and show that x = P*y are eigenvectors of A. Homework Equations B = P^-1*A*P, x = P*y The Attempt at a Solution I...
  45. M

    MHB Determine a matrix C such that T = CA has echelon form

    Hey! :o Let $$A=\begin{pmatrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{pmatrix}\in \mathbb{R}^{3\times 3}$$ I want to determine a matrix $C\in GL_3(\mathbb{R})$ such that $T:=C\cdot A$ has echelon form. Performing an elementary row operation is equivalent to multiplying an invertible matrix...
  46. kenneththo85431

    Describing Electronic orbit in 3D space using A matrix.

    I've plotted out the trajectory of an imaginary electron in 3D; next I represent it's points with the matrix A(x1 y1 z1) "throughout it's orbit": ( -1/2 -1 1 ( -2 -1.5 2 (-1/2 2 3...
  47. evinda

    MHB Solving the Matrix Transformation: $B \to C$

    Hello! (Wave) Let $B=(b_1, b_2)$, $C=(c_1, c_2)$ basis of $\mathbb{R}^2$ and $L$ operator of $\mathbb{R}^2$, the matrix as for $B$ of which is $\begin{pmatrix} 2 & 2\\ 1 & 0 \end{pmatrix}$. If $b_1=c_1+2c_2+b_2=c_1+3c_2$ and $A=\begin{pmatrix} a_{11} & a_{12}\\ a_{21} & a_{22} \end{pmatrix}$...
  48. U

    Projection Matrix Homework: Equations & Solution

    Homework Statement [/B]Homework EquationsThe Attempt at a Solution The solution is obviously given, but I don't really understand what is done there. What method is being used? so I can understand, because i see how they attained v, but then that vector normalised is not correct is it?
  49. CharlieCW

    Transforming one matrix base to another

    Homework Statement The SO(3) representation can be represented as ##3\times 3## matrices with the following form: $$J_1=\frac{1}{\sqrt{2}}\left(\matrix{0&1&0\\1&0&1\\ 0&1&0}\right) \ \ ; \ \ J_2=\frac{1}{\sqrt{2}}\left(\matrix{0&-i&0\\i&0&-i\\ 0&i&0}\right) \ \ ; \ \...
  50. mertcan

    A Matrix norm and Matrix measure

    Hi, initially I would like to share this link: https://books.google.com.tr/books?id=gWeVPoBmBZ8C&pg=PA25&lpg=PA25&dq=matrix+measure+properties&source=bl&ots=N1unizFvG6&sig=kxijoOVlPAacZDEdyyCwam4RQnQ&hl=en&sa=X&ved=2ahUKEwjd7o-Ap53dAhWJGuwKHdRbAO04ChDoATABegQICBAB#v=onepage&q=matrix measure...
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