Eigenvalues Definition and 820 Threads

Hi there this is my first post here, I am having some trouble with a homework question in quantum. I need to normalize both ψ1 and ψ2 and then find the energy eigenvalues of each. The given Hamiltonian is H0 = (1 2 ) (2 -1) And ψ1 = (...

Let's say I have the equation p(t)f''(t)=Kf(t) with p(t) a known periodical function, K an unknown constant and f(t) the unknown function. This is an eigenvalues problem that once solved gives a set of K={k1, k2,...} eigenvalues. I get these eigenvalues and they coincide with the ones...

This question is about the use of eigenvalues in a specific application. The subject is Computer Vision and the topic is the Harris Corner detection method. The attached file is PDF document of slides that show the math in a bit more detail. In the slides, a corner is located by looking at...

Homework Statement Find the eigenvalues of B = [5 2 0 2], [3 2 1 0], [3 1 -2 4], [2 4 -1 2]. Compute the sum and product of eigenvalues and compare it with the trace and determinant of the matrix. Homework Equations The Attempt at a Solution I get the characteristic polynomial...

Background: I'm having trouble using principal component analysis to try and align two data sets. I have two sets of 3D point data, and I can use PCA to get principal axes of the two sets of data. I do this by finding the eigenvectors of the covariance matrix for each set of data. This gives...

Just wondering is there a way to get the characteristic equation of an n by n matrix without going through tedious calculations of solving multiple determinants of matrices?

Homework Statement compute and plot the 10 lowest energy eigenvalues of a particleinan infinity deep spherically symmetric square well? Homework Equations The Attempt at a Solution

Hi How can i compute(or obtain from mathmatical tables) and plot a several energy eigenvalues of a particle in an infinity deep ,spherically and symmetric square well?

Homework Statement Hi all. I am given by following linear system: \begin{array}{l} \dot x = dx/dt = ax \\ \dot y = dy/dt = - y \\ \end{array} The eigenvalue of the matrix of this system determines the stability of the fixpoint (0,0): A=\left( {\begin{array}{*{20}c} a & 0 \\...

Am I understanding this right? Let's say I have a 15x15 matrix called Z. Then the matrix of eigenvalues calculated from Z, called D, can have two forms - either diagonal or block diagonal. If the matrix D comes out with values only on the diagonal, then there are only real values. But...

Homework Statement I am studying about eigenvalues and norms. I was wondering whether the way I understand them is correct. Homework Equations The Attempt at a Solution The eigenvalue of a matrix those that satisfy Ax = \lambda x, where A is a matrix, x is an eigenvector, \lambda...

Homework Statement C is an operator that changes a function to its complex conjugate a) Determine whether C is hermitian or not b) Find the eigenvalues of C c) Determine if eigenfunctions form a complete set and have orthogonality. d) Why is the expected value of a squared hermitian...

can somebody help me with the solution of the following problems? Ques. Find the eigenfunctions and eigenvalues for the operators 1. sin d/d psi 2. cos(i d/d psi) 3. exp(i a d/d psi) 4. (d)square/d (x)square+z/x * d/dx

It seems to be true, that if some eigenvalue of a Hamilton's operator is an isolated eigenvalue (part of discrete spectrum, not of continuous spectrum), then the corresponding eigenstate is normalizable, and on the other hand, if some eigenvalue of a Hamilton's operator is not isolated, then the...

Hello, Is it sufficient to determine that a nXn matrix is not diagonalizable by showing that the number of its distinct eigenvalues is less than n? Thanks for your time.

my question is take A= {(5,0,-1),(2,3,-1),(4,0,1)} find all eigenvalues and eigenvectors by using the characteristic equation i get -(lamda-3)3 however its the next bit i don't understand, in the answers (A-3I)(x,y,z)=(0,0,0) is used which I'm perfectly ok with and then (A-3I)2 is used and...

g(x,y) = x^3 - 3x^2 + 5xy -7y^2 Hessian Matrix = 6x-6******5 5********-7 Now I have to find the eigenvalues of this matrix, so I end up with the equation (where a = lambda) (6x - 6 - a)(-7 - a) - 25 = 0 Multiplying out I get: a^2 - 6xa + 13a - 42x + 17 = 0 How am I supposed to solve...

Matrix A= 1 2 0 2 1 0 2 -1 3 i got eigenvalues k=3 k=-1 what do i do after that to prove it is not able to be diagonalized

Homework Statement Hey guys, for my linear algebra class I need to find the signs of the eigenvalues (I just need to know how many are positive and how many are negative) of an nxn matrix with zeros everywhere except for the two diagonals directly above and directly below the main diagonal...

Hi, everyone! While I was studying for my midterm, I encountered this question. ------ Consider the hermitian operator H that has the property that H4 = 1 What are the eigenvalues of the operator H? What are the eigenvalues if H is not restricted to being Hermitian? ------ What I am...

Homework Statement alright, so i have a question which asks me to find the eigenvalues of a 3x3 square matrix A. after working on it for a long time, i can't figure it out, i know the process of it and i can do 2x2 matrices easily, i cannot figure this one out though. here is the matrix A; 2...

Homework Statement I have the hamiltonian : H=C(|2><1|+|1><2|) where : C=costant |1> and |2> are eigenstates of an osservable A. what are the eigenstate and eigenvalues of the hamiltonian? what is the probability that the system is in the state |2>? The Attempt at a Solution...

there is a equation for two spins in entangled Hamiltonian: H=J(\vec{\sigma}^1\cdot\vec{\sigma}^2+\vec{\sigma}^2\cdot\vec{\sigma}^1)+B(\vec{\sigma}^1_z+\vec{\sigma}^2_z) where \vec{\sigma}^i=(\sigma^i_x,\sigma^i_y,\sigma^i_z) are the pauli matrics for the ith (i=1,2) spin. J is the exchange...

Homework Statement Suppose that the 2x2 matrix A has eigenvalues lambda = 1,3 with corresponding eigenvectors [2,-1]^T and [3,2]^T. Find a formula for the entries of A^n for any integer n. And then, find A and A^-1 from your formula. Homework Equations Ax = lambda X (P^-1)AP = D A =...

The question is asking for what values of x will the matrix have at least one repeated eigenvalue (algebraic multiplicity of 2 or greater). The matrix is | 3 0 0 | | 0 x 2 | So naturally a normal attempt to find the eigenvalue in a question with only intergers | 0 2 x | I would continue...

If you had an operator A-hat whose eigenvectors form a complete basis for the Hilbert space has only real eigenvalue how would you prove that is was Hermitian?

Homework Statement Matrix A is -4 4 4 -4 4 4 4 -4 -4 It has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis of each eigenspace. The Attempt at a Solution I got the eigenvalues: the one of multiplicity 1 is -4 the one of multiplicity...

Homework Statement With knowledge of the orthogonality conditions for eigenfunctions with discrete eigenvalues, determine the orthonormal set for eigenfunctions with continuous eigenvalues. Use the definition of completeness to show that | a(k) |^2 = 1. 2. The attempt at a solution The first...

Suppose for a given matrix A, Sarah finds the eigenvectors v1 = [1 3 4 5]' and v2 = [5 6 3 4]' form a base for eigenspace of labmda = 2. Now suppose Janie finds the eigenvectors v3 = [1 2 2 3]' and v4 = [7 8 7 6]' form a base for eigenspace of lambda = 4. Is Janie's solution compatible with...

All I want to know is if a number and its negative appear as eigenvalues of a matrix, are they considered distinct? I have 4,1,-2,3 and -1 as eigenvalues of a particular matrix, but I can't get 5 linearly independent eigenvectors (to diagonalise the original matrix). I've plugged away and...

Homework Statement Consider two Ising spins coupled together −βH = h(σ1 + σ2) + Kσ1σ2, where σ1 and σ2 commute and each independently takes on the values ±1. What are the eigenvalues of this Hamiltonian? What are the degeneracies of the states? The Attempt at a Solution Four possible...

a) Let M be a 3 by 3 orthogonal matrix and let det(M)=1. Show that M has 1 as an eigenvalue. Hint: prove that det(M-I)=0. I think I'm supposed to begin from the fact that det(M)=1=det(I)=det(MTM) and from there reach det(M-I)=0 which of course would mean that there's an eigenvalue of 1 as...

Hi This is more of a math question but in the context of Quantum Mechanics, hence I posted it here. Suppose I have a matrix A of order 3x3 with three eigenvalues: 0, 0, 5. I am supposed to find the diagonalizing matrix for A. I know that in general, if P denotes the matrix of eigenvectors of...

Totaly stuck on this one can't even start to fathom an attempt. first part of the question is show that the eigenvalues of the matrix (2x2 left to right) 4,-1,-4,4 are sigma1=2 and sigma2 =2 and eigenvectors e1= (1,2)T and e2=(1,-2)T done this no problem but am writing this as the second part of...

How to get eigenvalues & eigenvectors of N x N matrix? Please can anyone help me out i have searched a lot but not able to find the solution. Regards

Is this a correct realization? The eigenspaces corresponding to the eigenvalues of A are the same as the eigenspaces corresponding to the eigenvalues of A^-1, transpose of A, and A^k for any k > 1. It took me some time to realize this but the v's, when you manipulate these equations, don't...

I wasn't sure about this question on my exam. Let eigenvalues be 0, 1, -1 Is it true that a. Not Invertible b. Diagonalizable c. Orthogonal a. True, since the determinant is 0 b. I'm not sure, but I chose False b/c I had an eigenvalue of 0 c. True, ah not sure either LOL!

Assuming 2 by 2. Ok, I'm asked to find the Eigenvalues. How do I know which should be lambda 1 and lambda 2? I can find the lambda's easily, but does it matter which is 1 or 2? It becomes important when I'm asked to diagonalize. A=S\Lambda S^{-1}

I just finished Differential Equations, and I know how to find eigenvalues/eigenvectors, and I understand how to use them to solve a differential equation. But I don't really understand "what they are". How is a matrix with complex eigenvalues any different than a matrix with real...

[SOLVED] Approximate eigenvalues Homework Statement Use some QR method to approximate the eigenvalues of [4 3] [3 5] and compare with the actual values. The actual values are (9±√37)/2 Homework Equations A(0)=Q(0)R(0) A(1)=R(0)Q(0) A-α(0)I=Q(0)R(0) A(1)=R(0)Q(0) + α(0)I...

[SOLVED] Positive Definite Matrices a) If A is Symmetric show that A-λI is positive definite if and only if all eigenvalues of A are >λ, and A-λI is negative definite if and only if all eigenvalues of A are <λ. b) Use this result to show that all the eigenvalues of [ 5 2 -1 0] [ 2 5 0...

[SOLVED] Approximate eigenvalues Use some QR method to approximate the eigenvalues of [4 3] [3 5] and compare with the actual values. The actual values are (9±√37)/2

Hi folks! I wasn't sure where to put this... so I put it here! I'm wondering if there is a physical interpretation/significance of the eigenvalues for a system? I've had people tell me things like "they're the basic solutions to the system" but I just don't quite see what they're saying...

This is a concept question.. I'm having trouble understanding why for an n x n matrix A, in order to have eigenvalues, it must have linearly dependent columns (so that a nontrivial solution exists), but for the same A, in order to be diagonalizable, the columns must be linearly INdependent...

Homework Statement Obtain the eigenvalues and corrosponding eigenvectors for the matrix: [2,2,1;1,3,1;1,2,2] Homework Equations The Attempt at a Solution I can solve for the eigenvalues, 5, 1, and 1 I can solve the eigenvalue 5 for the eigenvector B[1;1;1] Yet somehow, the...

Can someone please explain multiplicity to me? I've been able to solve the problems involving it, but I'm not quite sure what it means in terms of the eigenvalue. Thanks.

2. Write a MATLAB® function to calculate the condition number of a symmetric square matrix of any size by means of Eigenvalues: § The power method should be used to calculate the Eigenvalues. § The script (function) should give an error message if the matrix is not...

a) Consider the operator x d/dx(where 1st d/dx acts on the function, then x acts on the resulting function by simply multiplying by x )acting on the set of functions of a real variable x for x>0. What are the eigenvalues and the corresponding eigenfunctions of this operator? b) What about...

a) Consider a linear operator L with 2 different eigenvalues a1 and a2, with their corresponding eigenfunction f1 and f2. Is f1 + f2 also an eigenfunction of L? If so, what eigenvalue of L does it correspond to? If not, why not? b) Answer the same question as in part (a) but for the...

1) f(x,y,z)=x3-3x-y3+9y+z2 Find and classify all critical points. I am confused about the following: The Hessian matrix is diagonal with diagonal entries 6x, -6y, 2. Now, the diagonal entries of a diagonal matrix are the eigenvalues of the matrix. (this has to be true, it is already...