Matrix Definition and 1000 Threads

I have a .txt file which is 50 rows x 50 columns filled with entirely 0's and 1's. I have tried to plot the data with and without spaces between each column. I keep getting this message: gnuplot> splot 'C:\Users\raf\Desktop\PolymerProject\monte carlo code\directionInitial.txt' with pm3d...

Hello I was learning about determinants and matrices. I learned the generalization of getting the determinant of an n by n matrix. I then applied this to vector space (i + j + k) via a cross product and noticed that you leave the i j and k in their own columns in the first row of the matrix...

I've been using rotation matrices for quite some time now without fully grasping them. Whenever I tried to develop an intuitive understanding of... x' = x\cos\theta - y\sin\theta \\ y' = x\sin\theta + y \cos\theta ... I failed and gave up. I've looked at numerous online texts and videos, but...

Homework Statement Consider the linear transformation T from V = P2 to W = P2 given by T(a0 + a1t + a2t2) = (−4a0 + 2a1 + 3a2) + (2a0 + 3a1 + 3a2)t + (−2a0 + 4a1 + 3a2)t^2 Let E = (e1, e2, e3) be the ordered basis in P2 given by e1(t) = 1, e2(t) = t, e3(t) = t^2 Find the coordinate matrix...

Homework Statement The weighted vector norm is defined as ##||x||_W = ||Wx||##. W is an invertible matrix. The induced weighted matrix norm is induced by the above vector norm and is written as: ##||A||_W = sup_{x\neq 0} \frac{||Ax||_W}{||x||_W}## A is a matrix. Need to show ##||A||_W =...

Homework Statement Let u1,u2,u3 be an orthonormal basis for R3 and consider M as the plane with equation x1+2x2-2x3=0. Find the matrix of orthogonal reflection in that plane with respect to the given basis. Homework EquationsThe Attempt at a Solution In previous exercises , I had a matrix A...

Dear all, I want to know how to convert operator matrix when using Dirac Bra-Ket notation when it must be converted into a new dimension. I am currently working on transition dipole moment operator matrix D which I am going to use the following one: D = er Where e is charge of electron, r is...

Homework Statement $$ \begin{bmatrix} a &b \\ c&d \end{bmatrix}$$ I'm supposed to find the inverseHomework Equations Method of Gauss-Jordan The Attempt at a Solution So I tried putting zeros in this and I got the following : $$ \begin{bmatrix} ad-ac &0 &ad &ad-a \\ 0&bc-ad &c &-a...

Homework Statement Show that all square matrix (A whatever) can be written as the sum of a symmetric matrix and a anti symmetric matrix. Homework Equations I think this relation might be relevant : $$ A=\frac{1}{2}*(A+A^{T})+\frac{1}{2}*(A-A^{T}) $$ The Attempt at a Solution I know that we...

Homework Statement Check if L(p)(x)=(1+4x)p(x)+(x-x^2)p'(x)-(x^2+x^3)p''(x) is a linear transformation on \mathbb{R_2}[x]. If L(p)(x) is a linear transformation, find it's matrix in standard basis and check if L(p)(x) is invertible. If L(p)(x) is invertible, find the function rule of it's...

Homework Statement Write in Vector-Matrix form then write the augmented matrix of the system. r + 2s + t = 1 r - 3s +3t = 1 4s - 5t = 3 Homework Equations The matrix to which the operations will be applied is called the augmented matrix of the system Ax = b, It is formed by appending the...

Homework Statement [/B] Find the limit as ##n \to \infty ## of ##U_n(a) =\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & a/n \\ 0 & -a/n & 1 \end{pmatrix}^n##, for any real ##a##. Homework EquationsThe Attempt at a Solution I find ##U =\begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos a & \sin a \\ 0 & -\sin a &...

Homework Statement Prove $$||UA||_2 = ||AU||_2$$ where ##U## is a n-by-n unitary matrix and A is a n-by-m unitary matrix. Homework Equations For any matrix A, ##||A||_2 = \rho(A^*A)^.5##, ##\rho## is the spectral radius (maximum eigenvalue) where ##A^*## presents the complex conjugate of A. U...

Homework Statement If Γ is a k-regular simple graph and Γ its directed double, show that the matrix ˜ S for Γ (as per the FEATURED ARTICLE ) is a multiple of the adjacency matrix ˜ for Γ. Find the multiple. Assume k > 1. The matrix S is the probability matrix. The probability of going from one...

Homework Statement Find a 3x3 matrix A that satisfies the following equation where x, y, and z can be any numbers. ## A \begin{vmatrix} x \\ y \\ z \end{vmatrix} = \begin{vmatrix} x + y \\ x - y \\ 0 \end{vmatrix}##Homework EquationsThe Attempt at a Solution I attempted to solve this like...

So, I was examining the ground state of a Bose-Hubbard dimer in the negligible interaction limit, which essentially amounts to constructing and diagonalizing a two-site hopping matrix that has the form H_{i,i+1}^{(n)} = H_{i+1,i}^{(n)} = - \sqrt{i}\sqrt{n-i+1}, with all other elements zero...

Hi, I am looking for the general form of 2x2 complex transformation matrix. I have the article, that says "the relative position of a self-adjoint 2x2 matrix B with respect to A as a reference (corresponding to the transformation from the eigenspaces of A to the eigenspaces of B) is determined...

Hello, I am kind of new to Matlab so the questions I will ask probably sound a bit basic. Anyways, here goes: I want to create the matrix below which has both constants and variables. How can I do this? I know how to create a normal matrix (e.g. B = [1 0 2; 3 4 5; 0 2 3]) but I don't know how...

What does it mean by "In the position representation -- in which r is diagonal" in the paragraph below? How can we show that? Does it mean equation (3) in http://scienceworld.wolfram.com/physics/PositionOperator.html? (where I believe the matrix is in the ##|E_n>## basis)

Hello fellow nerds, I've come across a math problem, where I'd like to find the solution vector of a NxN square matrix. It is possible to find a solution for a given N, albeit numbers in the matrix become very large for any N>>1, and numbers in the solution vector become very small. So it's not...

I want to construct a completely correlated chi^2. I have a two-dimensional dataset, and its basically like: {m1,m2,m3,m4} {a1,a2,a3,a4} {x0,x0,x0,x0} So m1-m4, a1-a4 are all different, but each x0 is the same. This happens when I am fitting 2D data, but it is required that the function goes...

Hi everyone, I need help for preparing a Hamiltonian matrix. What will be the elements of the hamiltonian matrix of the following Schrodinger equation (for two electrons in a 1D infinite well): -\frac{ħ^{2}}{2m}(\frac{d^{2}ψ(x_1,x_2)}{dx_1^{2}}+\frac{d^{2}ψ(x_1,x_2)}{dx_2^{2}}) +...

The induced matrix norm for a square matrix ##A## is defined as: ##\lVert A \rVert= sup\frac{\lVert Ax \rVert}{\lVert x \rVert}## where ##\lVert x \rVert## is a vector norm. sup = supremum My question is: is the numerator ##\lVert Ax \rVert## a vector norm?

Homework Statement I can't understand this paper. I understand the whole incidence matrix stuff, but I don't quiet get how it relates to the linear algebra. I don't know if this is allowed to do, but I will ask you questions line by line, so basically you will read the paper with me explaining...

Homework Statement Being f : ℝ4 → ℝ4 the endomorphism defined by: ƒ((x, y, z, t)) = (3x + 10z, 2y - 6z - 2t, 0, -y+3z+t) Determine the base and dimension of Im(ƒ) and Ker(ƒ). Complete the base you chose in Im(ƒ) into a base of R4. Homework Equations Matrix A: $$\begin {bmatrix} 3 & 0 & 10 &...

I'm doing an online course in quantum information theory, but it seems to require some knowledge of linear algebra that I don't have. A definition that popped up today was the definition of the absolute value of a matrix as: lAl = √(A*A) , where * denotes conjugate transpose. Now for a...

Can an orthogonal matrix involve complex/imaginary values?

Homework Statement Determine the values of h such that the matrix is the augmented matrix of a consistent linear system. 1 4 -2 3 h -6 The attempt at a solution The answer I got differs from the back of the book. I tried solving it by adding R1(4) to R2 1 3 -2 -4 h 8 becomes 1...

Hi, my high school students enjoy using the applet found here (http://pages.jh.edu/~virtlab/bridge/truss.htm) to design model (basswood) bridges for our annual regional contest. It seems to require firefox these days. Recently, some designs have been causing extremely large forces to be...

Homework Statement [/B] 1. I've been tasked with forming a 10 x 10 matrix with elements 0, 1, 2, 3, 4, 5,... and have it display properly. 2. Then, take this matrix and make a 2d-histogram out of it. Homework Equations Here is my code void matrix6( const int n = 10) { float I[n][n]; //...

Homework Statement Consider the LTI (A,B,C,D) system $$ \dot{x}= \begin{pmatrix} 0.5&0&0&0\\ 0&-2&0&0\\ 1&0&0.5&0\\ 0&0&0&-1 \end{pmatrix} x+ \begin{pmatrix} 1\\ 1\\ 0\\ 0 \end{pmatrix} u $$ $$ y= \begin{pmatrix} 0&1&0&1 \end{pmatrix} x $$ Determine if A is diagonalizable Homework EquationsThe...

Hello all, I have a matrix A and I am looking for it's eigenvalues. No matter what I do, I find that the eigenvalues are 0, 1 and (k+1), while the answer of both the book and Maple is 0 and (k+2). I tried two different technical approaches, both led to the same place. The matrix is...

Although strictly quantum mechanics is defined in ##L_2## (square integrable function space)， non normalizable states exists in literature. In this case, textbooks adopt an alternative normalization condition. for example, for ##\psi_p(x)=\frac{1}{2\pi\hbar}e^{ipx/\hbar}## ##...

I have a doubt... Look this matrix equation: \begin{bmatrix} A\\ B \end{bmatrix} = \begin{bmatrix} +\frac{1}{\sqrt{2}} & +\frac{1}{\sqrt{2}}\\ +\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{bmatrix} \begin{bmatrix} X\\ Y \end{bmatrix} \begin{bmatrix} X\\ Y \end{bmatrix} = \begin{bmatrix}...

Due to the definition of spin-up (in my project ), \begin{eqnarray} \sigma_+ = \begin{bmatrix} 0 & 2 \\ 0 & 0 \\ \end{bmatrix} \end{eqnarray} as opposed to \begin{eqnarray} \sigma_+ = \begin{bmatrix} 0 & 1 \\ 0 & 0 \\ \end{bmatrix} \end{eqnarray} and the annihilation operator is...

Homework Statement X= 1st row: (0, 1, 0, 0), 2nd row: (1, 0, 0, 0), 3rd row: (0, 0, 0, 1-i), 4th row: (0, 0, 1+i, 0) Find the eigenvalues and eigenvectors of the matrix X. Homework Equations |X-λI|=0 (characteristic equation) (λ is the eigenvalues, I is the identity matrix) (X-λI)V=0 (V is the...

There is something that I don't quite understand or want clarification. See John Wheeler article "100 years of the quantum" http://arxiv.org/pdf/quant-ph/0101077v1.pdf refer to page 6 with parts of the quotes read "so if we could measure whether the card was in the alpha or beta-states, we...

Homework Statement Let A(l) = [ 1 1 1 ] [ 1 -1 2] be the matrix associated to a linear transformation l:R3 to R2 with respect to the standard basis of R3 and R2. Find the matrix associated to the given transformation with respect to hte bases B,C, where B = {(1,0,0) (0,1,0) , (0,1,1) } C =...

If we have two square matrices of the same size P and Q, we can put one in the exponent of the other by: M = P^Q = e^{ln(P)Q} ln(P) may give multiple results R, which are square matrices the same size as P. So then we have: M = e^{RQ} which can be Taylor expanded to arrive at a final square...

Hello! (Wave) I want to solve the following linear programming problem: $$\min (5y_1-10y_2+7y_3-3y_4) \\ y_1+y_2+7y_3+2y_4=3 \\ -2y_1-y_2+3y_3+3y_4=2 \\ 2y_1+2y_2+8y_3+y_4=4 \\ y_i \geq 0, i \in \{ 1, \dots, 4 \}$$ $\begin{bmatrix} 1 & 1 & 7 & 2 & | & 3\\ -2 & -1 & 3 & 3 & | & 2\\ 2 & 2 & 8...

Let the operators ##\hat{A}## and ##\hat{B}## be ##-i\hbar\frac{\partial}{\partial x}## and ##x## respectively. Representing these linear operators by matrices, and a wave function ##\Psi(x)## by a column vector u, by the associativity of matrix multiplication, we have...

Happy new year. Why everybody uses this definition of rotation matrixR(\theta) = \begin{bmatrix} \cos\theta & -\sin\theta \\[0.3em] \sin\theta & \cos\theta \\[0.3em] \end{bmatrix} ? This is clockwise rotation. And we always use counter clockwise in...

Why isn't the second line in (5.185) ##\sum_k\sum_l<\phi_m\,|\,A\,|\,\psi_k><\psi_k\,|\,\psi_l><\psi_l\,|\,\phi_n>##? My steps are as follows: ##<\phi_m\,|\,A\,|\,\phi_n>## ##=\int\phi_m^*(r)\,A\,\phi_n(r)\,dr## ##=\int\phi_m^*(r)\,A\,\int\delta(r-r')\phi_n(r')\,dr'dr## By the closure...

Each set of constant numbers such as ##(v_1, v_2, v_3)## are the components of a constant Cartesian vector because by rotation of coordinates they satisfy the transformation rule. Can we consider each set of constant arrays ## a_{ij};i,j=1,2,3 ## as components of a Cartesian tensor? In other...

For a state |\Psi(t)\rangle = \sum_{k}c_k e^{-iE_kt/\hbar}|E_k\rangle , the density matrix elements in the energy basis are \rho_{ab}(t) = c_a c^*_be^{-it(E_a -E_b)/\hbar} How is it that in the long time limit, this reduces to \rho_{ab}(t) \approx |c_a|^2 \delta_{ab} ? Is there some...

How do you write a matrix such as below image in Latex, in this forum?

Hello! (Wave) We have that $q(x) \geq q_0>0, x \in [0,1], h>0$. Suppose that we have this $(N+1) \times (N+1) matrix$: $\begin{bmatrix} \frac{1}{h^2}+\frac{1}{h}+\frac{q(x_0)}{2} & -\frac{1}{h^2} & 0 & \cdots & 0 \\ -\frac{1}{h^2} & \frac{2}{h^2}+q(x_1) & -\frac{1}{h^2} & \cdots &0 \\ 0 &...

Hey all. I know that A^TA is positive semidefinite. Is it possible to achieve a positive definite matrix from such a matrix multiplication (taking into account that A is NOT necessarily a square matrix)?

Homework Statement Determine if the matrix is diagonalizable or not. A= [ 3 -1 ] [ 1 1 ] Homework Equations Eigenvalues = det(A-Iλ) determinant of a 2x2 matrix = ad-bc The Attempt at a Solution Eigenvalues = det(A-Iλ) [ 3 -1 ] - [ λ 0 ] = [ 3 -λ -1 ] [ 1 1 ] [ 0 λ ]...

Fredrik submitted a new PF Insights post Matrix Representations of Linear Transformations Continue reading the Original PF Insights Post.