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. 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...
  2. 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...
  3. 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...
  4. 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##...
  5. 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...
  6. 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...
  7. Cathr

    I How to find the matrix of the derivative endomorphism?

    We have ##B=(1, X, X^2, X^3)## as a base of ##R3 [X]## and we have the endomorphisms ##d/dX## and ##d^2/dX^2## so that: ##d/dX (P) = P'## and ##d^2/dX^2 (P) = P''##. Calculating the matrix in class, the teacher found the following matrix, call it ##A##: \begin{bmatrix} 0 & 1 & 0 & 0...
  8. C

    Calculating y-parameters (admittance matrix)

    Homework Statement Homework EquationsThe Attempt at a Solution I keep getting something over 0 for my Y_11. I'm not sure what I'm doing wrong. I thought the ideal transformer does not have an admittance or impedance matrix, which is why I should be getting something over 0 but the there...
  9. J

    Finding bound state and scattering matrix of Hamiltonian

    Given that the Hamiltonian is H = P^2/(2m) + aδ(X − x(naught)) + bδ(X + x(naught), where x(naught) is a positive number. Find the conditions for bound states to exist and calculate their energies. Find the scattering matrix for arbitrary values of a and b. Can someone help me solve this please.
  10. Y

    Linear Algebra - Incidence Matrix of an RLC Ckt

    <Moved from a homework forum. Template removed.> I can't find any documentation on how to do this. I remember in linear algebra how to find the incidence matrix of an electrical network of purely resistors. Put how do I find it of a RLC circuit with resistors, inductors, and capacitors? I can't...
  11. N

    I What is the definition of a matrix in function form?

    My teacher told me to find the definition of matrix which is in function form, but haven't seen it. The definition of matrix that I know is a rectangular arrangement of mn numbers, in m rows and n columns and enclosed within a bracket, but it is not right which my teacher wants. I want to know...
  12. S

    I Index Gymnastics: Matrix Representations & Rank-2 Tensor Components

    I'm trying to get the hang of index gymnastics, but I think I'm confused about the relationship between rank-2 tensor components and their matrix representations. So in Hartle's book Gravity, there's Example 20.7 on p. 428. We're given the following metric: ##g_{AB} = \begin{bmatrix} F & 1 \\...
  13. Avatrin

    Python How to Import and Manipulate Data from a Text File in Python?

    Hi Lets say I have a txt file with m rows with n columns of numbers of the form: Lets say I want to take every p'th row and take the second and third columns and turn it into a \frac{m}{p}\times 2 matrix. How would I go about doing that?
  14. Tspirit

    Quantum Textbook for density matrix and trace?

    I want a QM textbook which introduces detail knowledge of density matrix and trace (i.e. the average), who can recommend one for me? Thank you.
  15. M

    Linear Transformations if the design matrix

    Homework Statement given that X is an n × p matrix with linearly independent columns. And $$X^∗ = XA$$ where A is an invertible p × p matrix. a) Show that: $$X^*{({X^*}^TX^*)^-}^1{X^*}^T = X{(X^TX)^-}^1X^T$$ b) Consider two alternative models $$M : Y = Xβ + ε$$ and $$M^∗ : Y = X^∗β ^∗ +...
  16. F

    Are We Living in a Simulation Beyond Our Understanding?

    How we can be sure that we are not living in matrix kind of virtual reality where we even do not have our bodies but all we have is our brain kept in jar of some liquid ? then also how we can be sure that the history as we know it till the last microsecond is totally made up and has been...
  17. Telemachus

    Fortran Reading matrix elements from a file in Fortran77

    SOLVED Hi there. I have the elements of a matrix written in a txt file (in row major order). I need to read this matrix to use it in my fortran77 program. The text file contains the elements written in this way: A(1,1) A(1,2) ... A(1,N) ... A(N,N-1) A(N,N). I was thinking in doing a do loop...
  18. saadhusayn

    I Matrix for transforming vector components under rotation

    Say we have a matrix L that maps vector components from an unprimed basis to a rotated primed basis according to the rule x'_{i} = L_{ij} x_{j}. x'_i is the ith component in the primed basis and x_{j} the j th component in the original unprimed basis. Now x'_{i} = \overline{e}'_i. \overline{x} =...
  19. W

    I Finding the Kernel of a Matrix Map

    Hi All, I am trying to see if there is a "nice" ( relatively straightforward) way of finding the solution/kernel of the map : ##f(A)=A^n -Id ## , where A is an ## k \times k ## matrix and ##n## is a positive integer. Question: what is the kernel of this map? Cranking out matrix coefficients...
  20. M

    What is the derivative of a skew symmetric matrix?

    Homework Statement Need to prove that the derivative of a rotation matrix is a skew symmetric matrix muktiplied by that rotation matrix. Specifically applying it on the Rodrigues’ formula.Homework EquationsThe Attempt at a Solution I have shown that the cubed of the skew symmetric matrix is...
  21. L

    I Transforming a Matrix: Elementary Methods for Finite Fields

    I want to transform the first matrix below into the second one. The book ( Neutsch, "Coordinates") says this can be done by elementary transformation. I guess he means by some Gaussian elimination. But the entries of the matrix are from the finite field 2, so I can not multiply rows, that would...
  22. T

    Matrix Multiplication Homework: Equations and Solutions"

    Homework Statement Homework Equations Matrix multiplication. The Attempt at a Solution Answer given=4 What am I doing wrong??
  23. DeathbyGreen

    Mathematica Eigenvectors 4x4 Matrix in Mathematica

    Hi, I'm trying to calculate the eigenvectors of a 4x4 matrix, but I don't want the actual eigenvalues included in the solution, I simply want them listed as a variable. For example, I have the matrix: H_F = \left[ \begin{array}{cccc} \hbar\Omega&\hbar v_fk_- &0&0\\ \hbar...
  24. P

    Einstein summation convention and rewriting as a matrix

    Homework Statement The question asks us to write down the matrix represented by the following summation. 2. Homework Equations The question summation... $$\sum_{j,k=1}^{3} a_{ij}b_{jk}x_{k}$$ The Attempt at a Solution $$ \sum_{j,k=1}^{3} a_{ij}b_{jk}x_{k} =...
  25. C

    A Understanding Rank of a Matrix: Important Theorem and Demonstration

    It is the demonstration of an important theorem I do not succeed in understanding. "A matrix has rank k if - and only if - it has k rows - and k columns - linearly independent, whilst each one of the remaining rows - and columns - is a linear combination of the k preceding ones". Let's suppose...
  26. S

    A Reduced matrix element for 0_ --> 0+ forbidden beta decay

    Hello Basically i need some help or references on proving that Working with spherical tensors in a 0_ ---> 0+ forbidden beta decay could you please give me some hints on how to do this proof? Thank you
  27. J

    8*8 blue dot matrix led display's specifications

    Hey, I want to ask you about the array led component: 1.9mm(0.8’’)8*8 blue dot matrix led displays (model no:KWM-20882XBA). << Edit by Mentor to add link to datasheet >> https://cdn-shop.adafruit.com/datasheets/956datasheet.pdf I saw the technical data sheet but I couldn’t find the...
  28. S

    A Calculation a reduced matrix element using E-Wigner Th.

    Hello. I fail to follow one step in the process of calculating ⟨la∥Y(L)∥lb⟩ . The spherical harmonics Yma(L)(r) represent the 2L+1 components of the spherical tensor of rank L. Writing the Eckart-Wigner th. for M = 0 yields: (1) Also one can write (2) Coupling L and lb to l: (3) Thus...
  29. D

    Prove trace of matrix: Tr(AB) = Tr(BA)

    Homework Statement [/B] The trace of a matrix is defined to be the sum of its diaganol matrix elements. 1. Show that Tr(ΩΛ) = Tr(ΩΛ) 2. Show that Tr(ΩΛθ) = Tr(θΩΛ) = Tr(ΛθΩ) (the permutations are cyclic) my note: the cross here U[+][/+]is supposed to signify the adjoint of the unitary matrix U...
  30. M

    I Matrix Equation -- clarification about solving a system

    Hi PF! Just want to make sure I'm not crazy: if we're solving a system ##K a = \sigma^2 M a## where ##K## and ##M## are ##n\times n## matrices, ##a## an ##n\times 1## vector and ##\sigma## a scalar, then ##a## is unnecessary, and all we really need to solve is ##K=\sigma^2 M##, right?
  31. Telemachus

    I How do I know if a matrix is positive definite?

    Hi. I have a real tridiagonal symmetric matrix that comes from the discretization of a partial differential equation. The elements are given by: ##A_{i,j}=-\delta_{i-1,j}\kappa_{i-1/2,l}\frac{\Delta t}{h^2}+\delta_{i,j}\left[\frac{2}{c}+\frac{\Delta t}{2}\mu_{i,j}+\frac{\Delta...
  32. Telemachus

    Fortran Matrix times vector in Fortran

    Hi there. I wanted to ask this question, which is about efficiency in matrix times vector multiplication in fortran. When I have some matrix ##\hat A## and vector ##\vec{x}##, and I want to compute the matrix times vector ##\hat A \vec{x}=\vec{b}## in Fortran, what I do is, I build the array...
  33. J

    I Proving Matrix Exponential Theorem: Unipotent & Nilpotent

    Hi, I'm kind of stuck with this theorem stating that: if A is an unipotent matrix, then exp(log A) = A and also if X is nilpotent then log(exp X) = X Does anyone know any good approaches to prove this? I know that for unipotent A, logA will be nilpotent and that for nilpotent X, exp(X)...
  34. X

    I What is the C_l in the Fisher Matrix For An CMB Survey?

    I'm trying to construct a Fisher Forecast for the upcoming S4 CMB survey. I don't understand what the C_l is in this formula. It is H(z) and the Angular Distance? Or is it some covariance matrix and if it is a covariance matrix how do I calculate it considering the experiment hasn't been done...
  35. nightingale123

    I Why is there a Matrix A that satisfies F(x,y)=<Ax,y>?

    I'm having trouble understanding a step in a proof about bilinear forms Let ## \mathbb{F}:\,\mathbb{R}^{n}\times\mathbb{R}^{n}\to \mathbb{R}## be a bilinear functional. ##x,y\in\mathbb{R}^{n}## ##x=\sum\limits^{n}_{i=0}\,x_{i}e_{i}## ##y=\sum\limits^{n}_{j=0}\;y_{j}e_{j}##...
  36. Adgorn

    Proving properties of a 2x2 complex positive matrix

    Homework Statement Prove that a 2x2 complex matrix ##A=\begin{bmatrix} a & b \\ c & d\end{bmatrix}## is positive if and only if (i) ##A=A*##. and (ii) ##a, d## and ##\left| A \right| = ad-bc## Homework Equations N/A The Attempt at a Solution I got stuck at the first part. if ##A## is positive...
  37. parshyaa

    I Finding the inverse of a matrix using transformations?

    We use A = I.A as equation and then by transforming only A of LHS and I of RHS we come to I = P.A and we say that P is the inverse of matrix A My question is that why we only tranform A and I, why A of RHS is left as it is during the transformation, or why transformation do not take place in...
  38. SetepenSeth

    Transition Matrix of T

    Homework Statement Find the transition matrix ##P## of a transformation defined as ##T:ℝ_2→ℝ_3## ##T:\begin{bmatrix}a\\b\end{bmatrix} = \begin{bmatrix}a+2b\\-a\\b\end{bmatrix}## For basis ##B=\begin{bmatrix}1\\2\end{bmatrix},\begin{bmatrix}3\\-1\end{bmatrix}##...
  39. parshyaa

    I What does the multiplication of matrix represents?

    As we know that 2×3 = 2+2+2 = 6; so similarly what does matrix multiplication represents?
  40. TheQuestionGuy14

    Is a 'Glitch in the Matrix' Real?

    The Internet is full of different communities, one such community is the 'Glitch in the Matrix' community, it is a big community and even has its own reddit page. People here discuss glitches they have experienced during the day, hundreds of people post everyday. Some posts are things that would...
  41. M

    I Exploring the Identity Matrix in Multivariable Control Theory

    Hello everyone. Iam working on a course in multivariable control theory and I stumbled over the Identity Matrix. I understand what the identity matrix is, though the use of it is a mistery... I was reading about going from state space to transfer functions and I found this expressions...
  42. nightingale123

    Finding the Jordan canonical form of a matrix

    Homework Statement About an endomorphism ##A## over ##\mathbb{C^{11}}## the next things are know. $$dim\, ker\,A^{3}=10,\quad dim\, kerA^{2}=7$$ Find the a) Jordan canonical form of ##A## b) characteristic polynomial c) minimal polynomial d) ##dim\,kerA## When: case 1: we know that ##A## is...
  43. SetepenSeth

    Linear Algebra - Standard Matrix of T

    Homework Statement Let T: ℝ² → P² a linear transformation with usual operations such as T [1 1] = 1 - 2x and T [3 -1]= x+2x² Find T [-7 9] and T [a b] **Though I'm writing them here as 1x 2 row vectors , all T's are actually 2x1 column vectors (I didn't see a way to give them proper...
  44. topsquark

    MHB Nested Matrix Elements: Define \Gamma^{\dagger}?

    I posted this elsewhere and was sort of able to figure out a result myself, but 1) I didn't do it right, and 2) No one answered it anyway. I thought I'd give it a shot over here. The problem deals with nested matrices. The gamma matrices can be found here. My question deals with a "vector"...
  45. B

    B Associativity of Matrix multiplication

    ##\begin{align}[A(BC)]_{ij} &= \sum_r A_{ir}(BC)_{rj} \\ &= \sum_r A_{ir} \sum_s B_{rs}C_{sj}\\ &= \sum_r\sum_s A_{ir}B_{rs}C_{sj}\\ &= \sum_{s} (\sum_{r} A_{ir} B_{rs}) C_{sj} \\ &= [(AB) C]_{ij}\end{align}## How did it went from ##2## to ##3##. In general is there a proof that sums can be...
  46. B

    B Is AB Invertible If n < m and B has a Non-Trivial Kernel?

    If ##A## is ##m \times n## matrix, ##B## is an ##n \times m## matrix and ##n < m##. Then show that ##AB## is not invertible. Let ##R## be the reduced echelon form of ##AB## and let ##AB## be invertible. ##I = P(AB)## where ##P## is some invertible matrix. Since ##n < m## and ##B## is ##n...
  47. B

    Prove that a matrix can be reduced to RRE and CRE

    Homework Statement Let ##A## be an ##m \times n## matrix. Show that by means of a finite number of elementary row/column operations ##A## can be reduced to both "row reduced echelon" and "column reduced echelon" matrix ##R##. i.e ##R_{ij} = 0## if ##i \ne j##, ##R_{ii} = 1 ##, ##1 \le i \le...
  48. B

    Inverse of a Matrix: Find Solution for A

    Homework Statement Find the inverse of ##A = \begin{bmatrix} 1 & \dfrac12 & & \cdots && \dfrac1n \\\dfrac12 & \dfrac13 && \cdots && \dfrac1{n+1} \\ \vdots & \vdots && && \vdots \\ \dfrac1n & \dfrac1{n+1} && \cdots && \dfrac1{2n-1}\end{bmatrix}## Homework EquationsThe Attempt at a SolutionI...
  49. Akineton

    I Transformation matrix from Dirac to Weyl

    Hello friends, I'm trying to construct transformation matrix S such that it transforms Dirac representations of gamma matrices into Chiral ones. I know that this S should be hermitian and unitary and from this I arrived an equation with 2 matrices on the LHS (a known matrix multiplied by S from...
  50. B

    B Proof of elementary row matrix operation.

    Prove that interchange of two rows of a matrix can be accomplished by a finite sequence of elemenatary row operations of the other two types. My proof :- If ##A_k## is to be interchanged by ##A_l## then, ##\displaystyle \begin{align} A_k &\to A_l + A_k \\ A_l &\to - A_l \\ A_l &\to A_k + A_l...
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