Matrix Definition and 1000 Threads

Hello everybody! I was studying the Glashow-Weinberg-Salam theory and I have found this relation: $$e^{\frac{i\beta}{2}}\,e^{\frac{i\alpha_3}{2} \begin{pmatrix} 1 & 0 \\ 0 & -1 \\ \end{pmatrix}}\, \frac{1}{\sqrt{2}}\begin{pmatrix} 0\\ v \\ \end{pmatrix} =...

Hello, I follow the post https://www.physicsforums.com/threads/cross-correlations-what-size-to-select-for-the-matrix.967222/#post-6141227 . It talks about the constraints on cosmological parameters and forecast on futur Dark energy surveys with Fisher's matrix formalism. Below a capture of...

We define the application $T:P_2\rightarrow P_2$ by $$T(p)=(x^2+1)p''(x)-xp'(x)+2p'(x)$$ 1. Give the matrix $\displaystyle\left[T\right]_\infty^\infty$ in the standard basis $\alpha=(x^2,x,1)$ 2 Give the matrix $\displaystyle\left[T\right]_\infty^\infty$ where...

Let A be a n x n matrix with complex elements. Prove that the a(k) array, with k ∈ ℕ, where a(k) = rank(A^(k + 1)) - rank(A^k), is monotonically increasing. Thank you! :)

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...

Hello, I am working on Fisher's formalism in order to get constraints on cosmological parameters. I am trying to do cross-correlation between 2 types of galaxy populations (LRG/ELG) into a total set of 3 types of population (BGS,LRG,ELG). From the following article...

Can anyone illustrate for me matrix decomposition in a simple way?

Homework Statement Consider the following vectors, which you can copy and paste directly into Matlab. x = [2 2 4 6 1 5 5 2 6 2 2]; y = [3 3 3 6 3 6 3 2 3 2]; Use the vectors x and y to create the following matrix. 2 3 0 0 0 0 0 0 0 0 0 3 2 3 0 0 0 0 0 0 0 0 0 3 4 3 0 0 0 0 0 0 0 0 0 3 6 6 0...

Over in the thread The eight-queens chess puzzle and variations of it | Physics Forums I discovered that with a toroidal board, one with periodic boundary conditions, the amount of symmetries becomes surprisingly large (A group-based search for solutions of the n-queens problem - ScienceDirect)...

In the context of SM (##SU(3)_C\otimes SU(2)_L\otimes U(1)_Y##) the charge operator is ##Q_{SM} = T_3 + \frac{Y}{2}\mathbb{I}_2## and gives us the fermions charges. Here ##T_3=\frac{1}{2}\sigma_3## is the third ##SU(2)## generator. For example, assuming ##Y=-1## for the left lepton doublet...

Hey! :o Let $A$ be a $4\times 5$ matrix with rank $2$ and let $U$ be the corresponding row echelon form matrix. I want to check if the following statements are true or not. If $B$ is a $5\times 5$ invertible matrix, at least two of the columns of $B$ are not in the nulity of $A$. There...

Homework Statement Given the expression s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1> obtain the matrix representations of s+/- for spin 1/2 in the usual basis of eigenstates of sz Homework Equations s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1> S_{+} = \hbar...

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.

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 -...

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...

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!

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.

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...

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...

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...

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

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...

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)...

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...

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)+...

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...

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...

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.

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

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...

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?

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...

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...

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##...

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?

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) $\langle x, Ax\rangle \geq 0$...

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...

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 &...

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...

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...

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

<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...

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...

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...

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...

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...

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...

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...

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 *...

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...