Read about matrix | 114 Discussions | Page 1

  1. K

    Calculate the angle between the E-field and Current vectors in an anisotropic conductive material

    In a certain anisotropic conductive material, the relationship between the current density ##\vec j## and the electric field ##\vec E## is given by: ##\vec j = \sigma_0\vec E + \sigma_1\vec n(\vec n\cdot\vec E)## where ##\vec n## is a constant unit vector. i) Calculate the angle between the...
  2. S

    Setting Free variables when finding eigenvectors

    upon finding the eigenvalues and setting up the equations for eigenvectors, I set up the following equations. So I took b as a free variable to solve the equation int he following way. But I also realized that it would be possible to take a as a free variable, so I tried taking a as a free...
  3. S

    Matrix concept Questions (invertibility, det, linear dependence, span)

    I have a trouble showing proofs for matrix problems. I would like to know how A is invertible -> det(A) not 0 -> A is linearly independent -> Column of A spans the matrix holds for square matrix A. It would be great if you can show how one leads to another with examples! :) Thanks for helping...
  4. S

    Using a determinant to find the area of the triangle (deriving the formula)

    This is the question. The following is the solutions I found: I understand that the first line was derived by setting one vertex on origin and taking the transpose of the matrix. However, I cannot understand where the extra row and column came from in the second line. Can anyone explain how...
  5. S

    Finding the Determinant to find out if the matrix is invertible

    question: My first attempt: my second attempt: So I am getting 0 (the right answer) for the first method and 40 for the second method. According to the theorem, shouldn't the determinant of the matrix remain the same when the multiple of one row is added to another row? Can anyone explain...
  6. O

    I Rotation of functions

    I was solving a problem for my quantum mechanics homework, and was therefore browsing in the internet for further information. Then I stumbled upon this here: R is the rotation operator, δφ an infinitesimal angle and Ψ is the wave function. I know that it is able to rotate a curve, vector...
  7. Athenian

    Rotation Matrix and Vectors

    Below is the attempted solution of a tutor. However, I do question his solution method. Therefore, I would sincerely appreciate it if anyone could tell me what is going on with the below solution. First off, the rotation of the matrix could be expressed as below: $$G = \begin{pmatrix} AB & -||A...
  8. Parzeevahl

    Comp Sci Multiplication of two 2x2 matrices in Fortran

    I have tried to do this using arrays and do loops: program matrixmul implicit none real A(2, 2), B (2, 2), C (2, 2) integer i, j, k write (*, *) 'Input: First matrix' do i = 1, 2 do j = 1, 2 read (*, *) A (i, j) enddo enddo write (*, *) 'Input: Second...
  9. M

    Proof a property for a 3x3 matrix

    Let a 3 × 3 matrix A be such that for any vector of a column v ∈ R3 the vectors Av and v are orthogonal. Prove that At + A = 0, where At is the transposed matrix.
  10. stephchia

    Finding the linear mapping between homogeneous coordinates

    Homework Statement If I have an affine camera with a projection relationship governed by: \begin{equation} \begin{bmatrix} x & y \end{bmatrix}^T = A \begin{bmatrix} X & Y & Z \end{bmatrix}^T + b \end{equation} where A is a 2x3 matrix and b is a 2x1 vector. How can I form a matrix...
  11. 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...
  12. 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...
  13. 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...
  14. 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...
  15. 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...
  16. 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
  17. N

    Python Unitary transformation using Python

    I would like to ask about unitary transformation. UA(IV) UB*UA(IV) UAT(UB*UA(IV))=UB(IV) UB(IV)*(X) IVT(UB(IV)*(X))=UB(X) UBT*UB(X)=X From the information above, UAT,IVT and UBT are the transpose of the complex conjugate. The aim of this code is to get the value of X in the step 4. This is...
  18. Abhishek11235

    Proving the following properties

    Mentor note: Member warned that an attempt must be shown. 1. Homework Statement This question is from book Afken Weber, Mathematics for Physicist. An operator ##T(t + ε,t)## describes the change in the wave function from t to t + ##\epsilon## . For ##\epsilon## real and small enough so that...
  19. L

    Setting up a matrix from a linear equation

    Homework Statement I need some help with a question on my assignment. It asks to set up a matrix from the linear equations, y=25x+70 and y=35x+40. Homework Equations How do I set this matrix up? The Attempt at a Solution I think that I have to rewrite it as 25x-y=-70 and 35x-y=-40. But then...
  20. M

    Eigenvectors for a 3x3 matrix

    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...
  21. 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 $$\phi^\dagger\phi=\frac{\phi_R^2 +\phi_I^2}{2}$$...
  22. Pushoam

    Determinant of exponential matrix

    Homework Statement Homework Equations The 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...
  23. 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...
  24. 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...
  25. Pushoam

    Calculating Eigenvalues help

    Homework Statement Homework Equations The 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...
  26. 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...
  27. 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...
  28. 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...
  29. S

    I Frobenius Norm of a matrix

    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!