Matrix Definition and 1000 Threads

Homework Statement The SO(3) representation can be represented as ##3\times 3## matrices with the following form: $$J_1=\frac{1}{\sqrt{2}}\left(\matrix{0&1&0\\1&0&1\\ 0&1&0}\right) \ \ ; \ \ J_2=\frac{1}{\sqrt{2}}\left(\matrix{0&-i&0\\i&0&-i\\ 0&i&0}\right) \ \ ; \ \...

Hi, initially I would like to share this link: https://books.google.com.tr/books?id=gWeVPoBmBZ8C&pg=PA25&lpg=PA25&dq=matrix+measure+properties&source=bl&ots=N1unizFvG6&sig=kxijoOVlPAacZDEdyyCwam4RQnQ&hl=en&sa=X&ved=2ahUKEwjd7o-Ap53dAhWJGuwKHdRbAO04ChDoATABegQICBAB#v=onepage&q=matrix measure...

Homework Statement given the matrix https://scontent.fhlz2-1.fna.fbcdn.net/v/t1.15752-9/40882602_313421129235428_2500668957757800448_n.png?_nc_cat=0&oh=7f5d6372c263996c6a11969b072d1349&oe=5BF8F2B7 in RREF we see solution to this system is x1+x2+x3 = 0 in the textbook it says which solutions...

Hey guys, I've got this question, that I think I have figured out, but I'm not completely sure. Basically, I've got the following matrix to put into RREF. Not really a problem, but I'm not sure if I'm handling the variable incorrectly. $\begin{bmatrix} 1 &-1 &|1 \\ 3 &a &|3 \end{bmatrix}$...

...to give a number? https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/lecture-notes/MIT8_04S16_LecNotes5.pdf On page 6, it says, " Matrix mechanics, was worked out in 1925 by Werner Heisenberg and clarified by Max Born and Pascual Jordan. Note that, if we were to write xˆ...

Suppose we have the matrix $ \mathbf{N} = \begin{bmatrix} 4 & -2 \\ -2 & 1 \end{bmatrix}$ and $\mathbf{X} = \begin{bmatrix}x \\ y \end{bmatrix}$. I want to solve $\displaystyle \frac{d\mathbf{X}}{dt} = \mathbf{NX}$. The eigenvalues of the matrix are $\lambda_1, \lambda_2 = 0,5$ and eigenvectors...

To my understanding, a matrix is just a way of representing a system of equations in an organized format. So for example, if we have some system of equations, we can get them into standard form, and translate them into what's known as an augmented matrix. This is similar to using synthetic...

The context for the question is in the attachments (pg1.png, pg2.png, pg3.png), so there is some reading involved. Although, it is a short and simple read if anything. The inquiry is in (inquiry.png). My understanding of the situation is that Q(t) abides by the differential equation Q'(t)Q(t)T...

Dear Everybody, I am having some problem with one exercise. And the question states: Find the transformation Matrix R that describes a rotation by 60 degrees about an axis from the origin thru the pt (1,1,1). The rotation is clockwise as you look down toward the origin. I know the standard...

Dear Everybody, I am trying to learn about the electrodynamics. I am using the textbook, Introduction to Electrodynamics (2nd Ed) by D. J. Griffiths. I am working on the Problem 1.8. The question state: Prove that the two-dimensional rotation matrix perverse the length of A. (That is, show...

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...

Hi everyone First of all, I am a computer science student and I have a question regarding the polarization of light as stated in an article entitled "Multi-stage quantum secure communication using polarization hopping" by Rifai et al.,2015. Given the Mueller matrix: The input of light state is...

Is there formula that transforms a matrix into its row-reduced echelon form? I know I can get there by row operations. But isn't there be like a formula?

I am trying to use the k.p method to study quantum well band structure. One example Hamiltonian look like this [J. Appl. Phys., 116, 033709(2014)] where ##{{\hat k}_ \pm } = {{\hat k}_x} \pm i{{\hat k}_y}## and the matrix elements are function of ##{{\hat k}_i}## and if quantum well is grown...

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...

I am developing a FORTRAN code (.f90) which "ll calculate some matrix in some time interval (dt1=0.001) and these matrices have to be integrated in some time steps (dt=0.1). Though I am experience in FORTRAN 77, new to FORTRAN 90. I am unable to make dimension of matrix real (I think that is the...

Hello, I'm looking for the non-negative matrix factorization (NNMF) source code. I checked several linear algebra libraries (e.g., LaPack, mkl), but it seems that this subroutine is not available. Does anyone know where I can find this source code...

Hello, I'm looking for a way to create an approximate row-orthonormal matrix with the number of rows (m) > the number of columns (n); i.e., finding A(mxn) so that A(mxn) . A^T(nxm) = I(mxm). I used singular value decomposition (e.g., DGESVD in mkl mathlib), but what I actually got was an...

Homework Statement Hi, guys. The question is: For a 3-state system, |0⟩, |1⟩ and |2⟩, write the matrix representation of the raising operators ## \hat A, \hat A^\dagger ##, ## \hat x ## and ##\hat p ##. Homework Equations I know how to use all the above operators projecting them on...

Suppose I have a vector space V and a matrix M such that multiplying every vector in V by M creates another vector space W. Now suppose I have another matrix A that I can also use to change vectors in V into other vectors. Does there exist a third matrix B such that - for any vector v1 in V -...

Homework Statement Homework EquationsThe Attempt at a Solution I know I would have to do something with my calculator and I tried to solve like solving an equation for C, but not sure. I put all the matrices in my calculator. I then subtracted the first matrix to the other side then...

I understand the dot product of ei.ej, but I can't find the matrix components.

Can someone explain to me how is it possible for D-branes to be parametrized with matrix coordinates? I mean, D-brane is a surface embedded in ordinary space, no? And the coordinates of ordinary space are vectors. So how can those vector coordinates suddenly turn into matrix ones on a D-brane?

Mentor note: Thread moved from Mathematics section, so is missing the HW template John and Eli are playing a game with a hall that can roll into one of two pockets labelled H and Y. John wants to keep the hall in H and Eli wants to keep it in Y. When it is John's turn to play, ifhe finds the...

Homework Statement A beam of neutrons (moving along the z-direction) consists of an incoherent superposition of two beams that were initially all polarized along the x- and y-direction, respectively. Using the Pauli spin matrices: \sigma_x = \begin{pmatrix} 0 & 1 \\ 1 & 0 \\...

For an anisotropic material, is there any way to analytically determine the elements of the stiffness matrix? For orthotropic and isotropic materials, there are analytical expressions relating the stiffness matrix elements to the elastic modulus and poisson's ratio, but I do not believe this...

Homework Statement Homework Equations None. The Attempt at a Solution I know that the standard matrix of a counterclockwise rotation by 45 degrees is: [cos 45 -sin 45] [sin 45 cos 45] =[sqrt(2)/2 -sqrt(2)/2] [sqrt(2)/2 sqrt(2)/2] But the problem says "followed by a projection onto the line...

I understand that a normal matrix has a complete, canonical eigendecomposition in which the normalized modal eigenvector matrix is unitary, and this its inverse is simply the transpose, and the modal eigenvalue matrix is diagonal (let's presume distinct eigenvalues). But I wonder if there is...

Homework Statement Costruct a: The Attempt at a Solution I found 3 equations but i miss another one :( M=\begin{bmatrix} a & b\\ c & d \end{bmatrix} (1) a+d = 0 from the definition of nilpotent matrix (2) a+3b = 0 from kernel (3) c +3d= 0 from kernel

If matrix has integer entries and it is hermitian, are then eigenvalues also integers? Is there some theorem for this, or some counter example?

Homework Statement I have to costruct a 2x2 matrix so that : The Attempt at a Solution M =\begin{bmatrix} a & b\\ c &d \end{bmatrix} Using the first bond i got : c+2d = 2a+4b (1) using the second bond : d = -b (2) And then, as a nilpotent matrix has det = 0 and tr = 0, i got a+d-2=0 (3)...

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 I...

Homework Statement Form unitary matrix from eigen vectors of ##\sigma_y## and using that unitary matrix diagonalize ##\sigma_y##. \sigma_y= \begin{bmatrix} 0 & -i & \\ i & 0 & \\ \end{bmatrix}[/B]Homework Equations Eigen vectors of ##\sigma_y## are...

So, I recently came across this example: let us "define" a function as ƒ(x)=-x3-2x -3. If given a matrix A, compute ƒ(A). The soution proceedes in finding -A3-2A-3I where I is the multiplicative identity matrix. Now , I understand that you can't add a scalar and a matrix, so the way I see it is...

Given matrices A,B and Condition 1: AB does not equal BA Condition 2: A and B do not have common eigenvectors are these two conditions equivalent? If not, exactly how are they related? Since I'm thinking about quantum mechanics I'm wondering specifically about Hermitian matrices, but I'm...

AIUI, every normal matrix has a full eigenvector solution, and there is only 1 *normalized* modal matrix as the solution (let's presume unique eigenvalues so as to avoid the degenerate case of shared eigenvalues), and the columns of the modal matrix, which are the (normalized) eigenvectors, are...

Is the Lorentz transformation matrix Λμν a tensor of order two and does it transform like a tensor ?

Homework Statement Suppose that A is a 3 x n matrix whose columns span R3. Explain how to construct an n x 3 matrix D such that AD = I3. "Theorem 4" For a matrix A of size m x n, the following statements are equivalent, that is either all true or all false: a. For each b in Rm, Ax = b has a...

Hi PF! Let's say I have a 3X3 matrix ##K## and a much larger square matrix, call it ##M##. I am trying to add ##K## into ##M## along the diagonals. It's difficult for me to explain (and hence code) so I've attached a picture. Does anyone know a good way of doing this? Notice overlap is only in...

$\textsf{Find the inverse of matrix} $ $$A=\left| \begin{array}{rrr} 1&0&2\\ 1&0&0 \\ 3&2&0 \end{array} \right|$$ $\textsf{by method of adjoint matrix }\\$ $\textsf{adj $A = |C_{ij}|^T$}\\$ $\textsf{det $A =4$}\\$ $\textsf{so then}\\$ $A^{-1}=\frac{1}{det A}(adj A)= \frac{1}{4}(adj A)$...

I am reading Leonard Susskind's Theoretical Minimum book on Quantum Mechanics. Excercise 7.4 is as follows: Calculate the density matrix for ##|\Psi\rangle = \alpha|u\rangle + \beta|d\rangle##. Answer: $$ \psi(u) = \alpha, \quad \psi^*(u) = \alpha^* \\ \psi(d) = \beta, \quad \psi^*(d) =...

Homework Statement Please see attached file. I'm not quite sure if I'm on the right track here. I think the basis for F is throwing me off as well as T(f). Please advise. Thanks! Homework EquationsThe Attempt at a Solution

I am trying to see how to derive the following inequality on page 36 in the proof of Lemma 11.3: https://arxiv.org/pdf/math/0412040.pdf I.e, of: $$\| fg \|_{Lip} \le \bigg(1+\ell \sup_{t\in T} |g'(t)|\bigg)\sup_{t\in T}|f'(t)| , \ \ supp \ f(1-g)\subset S^c$$ My thoughts about how to show...

Post moved by moderator, so missing the homework template. series ##{a_n}## is define by ##a_1=1 ## , ##a_2=5 ## , ##a_3=1 ##, ##a_{n+3}=a_{n+2}+4a_{n+1}-4a_n ## ( ##n \geq 1 ##). $$\begin{pmatrix}a_{n+3} \\ a_{n+2} \\ a_{n+1} \\ \end{pmatrix}=B\begin{pmatrix}a_{n+2} \\ a_{n+1} \\ a_{n} \\...

A problem that I have to solve for my Linear Algebra course is the following We are supposed to use Mathematica. What I have done is that I first checked that A is symmetric, i.e. that ##A = A^T##. Which is obvious. Next I computed the eigenvalues for A. The characteristic polynomial is...

Hi, in first attachment/picture you can see the generalized navier stokes equation in general form. In order to linearize these equation we use Beam Warming method and for the linearization process we deploy JACOBİAN MATRİX as in the second attachment/picture. But on my own I can ONLY obtain the...

Good day All, while trying to solve this exercice I was puzzeld by the solution approach indeed, they use the symmetry of the structure, they have made a cut on the hinge where the force F is applied (the force F has been divided by 2 for the symmetry reason), and ONLY replace it with a...

Hi, I guess this could be a rather silly question, but I got a bit confused about the "numerator layout notation" and "denominator layout notation" when working with matrix differentiation...

Given a real-valued matrix ## \bar{B}_2=\begin{bmatrix} \bar{B}_{21}\\ \bar{B}_{22} \end{bmatrix}\in{R^{p \times m}} ##, I am looking for an orthogonal transformation matrix i.e., ##T^{-1}=T^T\in{R^{p \times p}}## that satisfies: $$ \begin{bmatrix} T_{11}^T & T_{21}^T\\ T_{12}^T...

Homework Statement Obtain a 4×4 projection matrix that maps ##ℝ^3## to the plane 3x + 2y = 1. Assume that the centre of projection i.e. eye is at (0,0,0). The problem that my problem is strongly based on and its solution are #3, here. (I'm referring to the first way of solving the problem in...