# matrix

1. ### 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...
2. ### 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.
3. ### Finding the linear mapping between homogeneous coordinates

1. Homework Statement If I have an affine camera with a projection relationship governed by: $$\begin{bmatrix} x & y \end{bmatrix}^T = A \begin{bmatrix} X & Y & Z \end{bmatrix}^T + b$$ where A is a 2x3 matrix and b is a 2x1 vector. How can I form a matrix...
4. ### Find the eigenvalues and eigenvectors

1. Homework Statement Find the eigenvalues and eigenvectors of the following matrix: $$A = \begin{bmatrix} 3 & 0 & 0 \\ 0 & 3 & 2 \\ 0 & -1 & 0 \end{bmatrix}$$ 2. Homework Equations Characteristic polynomial: $$\Delta (t) = t^3 - Tr(A) t^2 + (A_{11}+A_{22} +A_{33})t - det(A) .$$ 3. The...
5. ### 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...
6. ### 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...
7. ### 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...
8. ### Show that a matrix is a Lorentz transformation

1. 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 $\beta = tanh(\psi)$ 2. Homework Equations During the...
9. ### 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
10. ### 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...
11. ### 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...
12. ### Setting up a matrix from a linear equation

1. 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. 2. Homework Equations How do I set this matrix up? 3. The Attempt at a Solution I think that I have to rewrite it as 25x-y=-70 and 35x-y=-40...
13. ### 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...
14. ### 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 $$\phi^\dagger\phi=\frac{\phi_R^2 +\phi_I^2}{2}$$...
15. ### Determinant of exponential matrix

1. Homework Statement 2. Homework Equations 3. The Attempt at a Solution 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...
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### 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 : $$\int x(t)\overline y(t) dt$$ on the x and y coordinates of the eigenvectors [x_1,y_1] and...
17. ### How to check if a transformation is surjective and injective

1. Homework Statement I have attached the question. Translated: Suppose T: R^4 -> R^4 is the image so that: ...... 2. 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...
18. ### Calculating Eigenvalues help

1. Homework Statement 2. Homework Equations 3. 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...
19. ### Trace of the Exponential of a Square Matrix

1. Homework Statement Find the trace of a $4\times 4$ matrix $\mathbb U=exp(\mathbb A)$, where $$\mathbb A = \begin {pmatrix} 0&0&0&{\frac {\pi}{4}}\\ 0&0&{\frac {\pi}{4}}&0\\ 0&{\frac {\pi}{4}}&0&0\\ {\frac {\pi}{4}}&0&0&0 \end {pmatrix}$$ 2. Homework Equations e^{(\mathbb A)}=\mathbb...
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### 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...
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### 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...
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### 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
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### 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!
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### A Use of the Radon transform on an ill-posed matrix

Hi, I have a script for generating a figure based on the radon transform of an ill-posed matrix. However, I have no idea what the radon transform is applied for, and how it is useful for matrix analysis. Can someone elucidate on what one gets out on applying a radon transform on an ill posed...
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### 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: ...
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### 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...
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### Constructing a 3x3 Linear system question

1. 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...
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### Reducing a matrix to echelon form

1. 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 2. Homework Equations Gaussian elimination I used here...
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### I Convert an ODE to matrix form

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...
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### 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...