Matrix Definition and 1000 Threads

I have questions regarding the 24 gauge bosons of the SU(5) model. I keep seeing this matrix popping up in the documents I'm reading with no real explanation of why: First of all I'm wondering how this is constructed, which means I'm wondering what the V_{\mu}^{a} look like (I already have...

In my school LA requires a pre req proof class vs matrix algebra which doesn't. Would matrix algebra even be worth taking?

Hi all, Firstly, I am not sure whether this is the area of the forum to ask this. I have been learning and researching a completely different topic, and from this I have come across a completely new concept of the Kronecker function. I have done a google search on this to get the intro and...

Homework Statement Find a 2X2 matrix that has all non-zero entries where 3 is an eigenvalue Homework EquationsThe Attempt at a Solution well since the 2x2 matrix cannot be triangular, it makes things harder for me. I have no idea where to start. I am not given any eigenvectors either. It seems...

Homework Statement A square matrix ##n\times n##, A, that isn't the zero-matrix have powers ##A^{k-1}## that isn't the zero matrix. ##A^k## is the zero matrix. What are the possible values for ##k##? Homework Equations N/A The Attempt at a Solution I'm a bit lost here but I figure that maybe...

Homework Statement Sakurai Modern Quantum Mechanics Revised Edition. Page 81. density matrix p = 3/4 [1 0; 0 0] + 1/4 [1/2 1/2; 1/2 1/2]. We leave it as an exercise to the reader the task of showing this ensemble can be decomposed in ways other than 3.4.24Homework Equations 3.4.24 w( sz +...

Homework Statement Show that strictly upper triangular ##n\times n## matrices are nilpotent. Homework EquationsThe Attempt at a Solution Let ##f## be the endomorphism represented by the strict upper triangular matrix ##M## in basis ##{\cal B} = (e_1,...,e_n)##. We have that ##f(e_k) \in...

Homework Statement Let ##U## be a ##2\times 2## orthogonal matrix with ##\det U = 1##. Prove that ##U## is a rotation matrix. Homework EquationsThe Attempt at a Solution Well, my strategy was to simply write the matrix as $$U = \begin{pmatrix} a & b\\ c & d \end{pmatrix}$$ and using the given...

I am reading a paper and am stuck on the following snippet. Given two orthonormal frames of vectors ##(\bf n1,n2,n3)## and ##(\bf n'1,n'2,n'3)## we can form two matrices ##N= (\bf n1,n2,n3)## and ##N' =(\bf n'1,n'2,n'3)##. In the case of a rigid body, where the two frames are related via...

This page (https://shiyuzhao.wordpress.com/2011/06/08/rotation-matrix-angle-axis-angular-velocity/), gives the following relation: \left[R\vec{\omega}\right]_{\times}=R\left[\vec{\omega}\right]_{\times}R^{T} Where: * ##R## is a DCM (Direction Cosine Matrix) * ##\vec{v}## is the angular...

Do you know any books or reviews that explains these in sufficient detail? I am having some small problems in understanding the triangles of the CKM matrix elements and experiments conducted for their measurement...

How many ways to arrange cells of k possible values in a mxn matrix provided that sums of all rows and columns are known? For example, if we have a 5x3 matrix and 10 possible values ( from 0 to 9) that can be assigned for each cell, then how many ways to arrange cells in that matrix satisfying...

Hello. I'm having trouble understanding what is required in the following problem: Find the relation between the matrix elements of the operators $\widehat{p}$ and $\widehat{x}$ in the base of eigenvectors of the Hamiltonian for one particle, that is, $$\widehat{H} = \frac{1}{2M} \widehat{p}^2...

Hi All, I have spent hours trying to understand the matrix form of Density Operator. But, I fail. Please see page 2 of the attached file. (from the book "Quantum Mechanics - The Theoretical Minimum" page 199). Most appreciated if someone could enlighten me this. Many thanks in advance. Peter Yu

Hi Folks, I am looking at Shankars Principles of Quantum Mechanics. For Hermitian Matrices M^1, M^2, M^3, M^4 that obey M^iM^j+M^jM^i=2 \delta^{ij}I, i,j=1...4 Show that eigenvalues of M^i are \pm1 Hint: Go to eigenbasis of M^i and use equation i=j. Not sure how to start this? Should I...

Hi Folks, I calculate the eigenvalues of \begin{bmatrix}\cos \theta& \sin \theta \\ - \sin \theta & \cos \theta \end{bmatrix} to be \lambda_1=e^{i \theta} and \lambda_2=e^{-i \theta} for \lambda_1=e^{i \theta}=\cos \theta + i \sin \theta I calculate the eigenvector via A \lambda = \lambda V as...

/How can I show that Potts model hamiltonian is equal to this matrix hamiltonian? Potts have these situations : { 1 or 1 or 1 or 0 or 0 or 0} but the matrix hamiltonian : { 1 or 1 or 1 or -1/2 or -1/2 or -1/2} I take some example and couldn't find how they can be equal.

I've seen various different matrices used to represent beam splitters, and am wondering which is the "right" one. Alternatively, are there various kinds of beam splitters but everyone just ambiguously calls them the same thing? The matrices I've seen are the...

Homework Statement Find a non zero matrix(3x3) that does not have in its range. Make sure your matrix does as it should.The Attempt at a Solution [/B] I know a range is a set of output vectors, Can anyone help me clarify the question? I'm just not sure specifically what its asking of me, in...

I calculate 1) ##\Omega= \begin{bmatrix} 1 & 3 &1 \\ 0 & 2 &0 \\ 0& 1 & 4 \end{bmatrix}## as not Hermtian since ##\Omega\ne\Omega^{\dagger}## where##\Omega^{\dagger}=(\Omega^T)^*## 2) ##\Omega\Omega^{T}\ne I## implies eigenvectors are not orthogonal. Is this correct?

Homework Statement [/B]Find the matrix that performs the operation 2x2 Matrix which sends e1→e2 and e2→e1Homework EquationsThe Attempt at a Solution [/B] I know e1 = < 1 , 0> and e2 = <0 , 1> Basically I'm not quite sure what the question is asking. This is the one of the problems I am...

Let A be a 2 X 2 matrix such that AX = XA for all 2 X 2 real matrices X. Show that A =kI for some k belonging to R

A difference matrix takes the entries of a vector and computes the differences between the entries like [x1 - 0 ] = difference from 0 and x1: 1 step [x2 - x1] = difference from x2 and x1: 1 step [x3 - x2] = difference from x3 and x2: 1 step assuming we had a vector x in Ax = b So why now when...

It's a new series on Netflix from those involved with Babylon 5 and the Matrix. Has anyone here seen it yet? What did you think about it?

Hi everyone I am trying to diagonalise a (2n+1)x(2n+1) matrix which has diagonal terms A_ll = (-n+l)^2 and other non vanishing terms are A_l(l+1) = A_(l+1)l = constant. Is there any way I can solve it for general n without having to use any numerical methods. I remember once a professor...

If I have two random variables X, Y that are given from the following formula: X= \mu_x \big(1 + G_1(0, \sigma_1) + G_2(0, \sigma_2) \big) Y= \mu_y \big(1 + G_3(0, \sigma_1) + G_2(0, \sigma_2) \big) Where G(\mu, \sigma) are gaussians with mean \mu=0 here and std some number. How can I find...

say for example when I calculate an eigenvector for a particular eigenvalue and get something like \begin{bmatrix} 1\\ \frac{1}{3} \end{bmatrix} but the answers on the book are \begin{bmatrix} 3\\ 1 \end{bmatrix} Would my answers still be considered correct?

Homework Statement Let A be the matrix \left(\begin{array}{cc}a&b\\c&d\end{array}\right), where no one of a, b, c, d is zero. It is required to find the non-zero 2x2 matrix X such that AX + XA = 0, where 0 is the zero 2x2 matrix. Prove that either (a) a + d = 0, in which case the general...

Hello everybody, Sorry to ask you something that may be easy for you but I'm stuck. For example I have 2 images (size 2056x2056). One image of reference and the other is the same rotated from -90degrees. Using a program with keypoints, it gives me a transform matrix : a=2.056884522e+03...

I have the following matrix R(x) = [cos(x) -sin(x) ; sin(x) cos(x)] Now consider the unit vectors v = [1;0] and w = [0,1]. Now if we compute R(x)v and R(x)w the vectors are supposed to rotate about the origin by the angle x in a counter clockwise direction. I am struggling to see how this...

Ok so officially a matrix is a rectangular array of numbers, symbols, etc arranged in rows and columns that is treated in certain prescribed ways. But that doesn't help me understand a darn thing. From what I understand, a matrix is a math tool that can help you solve linear systems, represent...

Homework Statement _ _ |1 0 0 0 -1 0 0 | 700 | |0 1 0 0 -1 0 0 | 500 | |0 0 1 0 0 0 0 0 | 150 | |0 0 0 1 0 1 0 | 1200 | |0 0 0 0 1 0 0 | -650 | |0 0 0 0 0 0 1 | -600 | Homework EquationsThe Attempt at a Solution This is driving me up the wall, am I missing...

Consider I+A*B where A: (n*l) is a variable matrix and B: (l*n) is known. I am looking for some way to find a sufficient condition for nonsingularity of I+A*B

Dear all, In this paper: http://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.125402 In the appendix the author attempts to arrive at the spectral density of states of the surface of a half-space. To do this, he arrives at the Green's function of the surface atom of 1D atomic chain and...

Hi Since a few days I've been confused about the seesaw mass matrix explaining neutrino masses. It is the following matrix: \begin{pmatrix} 0 & m\\ m & M \\ \end{pmatrix}. As can easily be checked it has two eigenvalues which are given by M and -m^2/M in the limit M>>m (the limit doesn't...

Hello Everyone, Can someone explain why do matrices with linearly independent columns have only 0 vector in their null space? Thanks

Could some please tell me if they think my answer for 1c and 3d of these questions I've done are right. thanks.

As a step in a solution to another question our lecture notes claim that the matrix (a,b,c,d are real scalars). \begin{bmatrix} 2a & b(1+d) \\ b(1+d)& 2dc \\ \end{bmatrix} Is positive definite if the determinant is positive. Why? Since the matrix is symmetric it's positive definite if the it...

Assume the mapping T: P2 -> P2 defined by: T(a0 + a1t+a2t2) = 3a0 + (5a0 - 2a1)t + (4a1 + a2)t2 is linear.Find the matrix representation of T relative to the basis B = {1,t,t2} My book says to first compute the images of the basis vector. This is the point where I'm stuck at because I'm not...

Homework Statement I. 3*3 matrix A (8 2 -2, 2 5 4, -2 4 5) II. 3*3 matrix (1 2 0, -1 -2 0, 3 5 1) Homework Equations I. Solve Aexp 100 of 3*3 II. Find the 5th rooth of B matrix The Attempt at a Solution I. I got stuck at diagonalising the matrix. Is this OK 1st step ? If yes...

Good afternoon all, I'm investigating typical values of entropy for a subsystem of a 1D (non-interacting) spin chain. Most of the problem is essentially solved I've shown that a typical pure state of the entire chain is close (trace norm) to the state ##\Omega_S## when reduced. \Omega_S =...

So, essentially, all I wonder is: What is the The Matrix Exponent of the Identity Matrix, I? Silly question perhaps, but here follows my problem. Per definition, the Matrix Exponent of the matrix A is, e^{A} = I + A + \frac{A^2}{2} + \ldots = I + \sum_{k=1}^{\infty} \frac{A^k}{k!} =...

Hi PF Peeps! Something came up while I was studying for my QM1 class. Basically we want to represent operators as matrices and in one case the matrix element is defined by the formula : <m'|m> = \frac{h}{2\pi}\sqrt{\frac{15}{4} - m(m+1)} \delta_{m',m+1} But the thing is we know m takes on...

Homework Statement \begin{array}{rrr|r} -1 & 2 & -1 & -3 \\ 2 & 3 & α-1 & α-4 \\ 3 & 1 & α & 1 \end{array} α∈ℝ for the augmented matrix, what value of α would make the system consistent? Homework Equations N/A Answer: α=2 The Attempt at a Solution I know that the system has to have an...

The GHZ state is: |\psi> = \frac{|000> + |111>}{\sqrt2} To calculate density matrix we go from: GHZ = \frac{1}{2}(|000> + |111>)(<000| + <111|) GHZ = \frac{1}{2}( |000><000| + |111><111| + |111><000| + |000><111|) To: GHZ = 1/2[ \left( \begin{array}{cc} 1 & 0 & 0 & 0 & 0 &...

Imagine applying an operator to a wave-function: \psi_t(x_1, x_2, ..., x_n) \rightarrow \frac{L_n(x)\psi_t(x_1, x_2, ..., x_n)}{||\psi_t(x_1, x_2, ..., x_n)||} Where ## \psi _t(x_1, x_2, ..., x_n) ## is initial system state vector, denominator is normalization factor, and Ln(x) is a...

Homework Statement If matrix ## C = \left[ {\begin{array}{c} A \\ B \ \end{array} } \right]## then how is N(C), the nullspace of C, related to N(A) and N(B)? Homework Equations Ax = 0; x = N(A) The Attempt at a Solution First, I thought that the relation between A and B with C is ## C = A...

Homework Statement Given the matrices A, B, C, D, X are invertible such that (AX+BD)C=CA Find an expression for X. Homework Equations N/A Answer is A^{-1}CAC^{-1}-A^{-1}BD The Attempt at a Solution I know you can't do normal algebra for matrices. So this means A≠(AX+BD)?

Hi people. I just read some articles about physicist starting to gain more and more evidence for the Universe to be a 3D Hologram of a 2D world (or that's how I understood it). And apparently for us living in a "Matrix", like the one in the movie. Now I would like to understand the relation...

I just couldn't understand how does augmented matrix deduce inverse of a matrix. I mean what is it in the row operation because of which we get the inverse of a matrix. I just don't want to learn the steps but to understand why it works. Thank you.