Eigenvalues Definition and 820 Threads

Let's say that I have to construct a 2 X 2 matrix from a second-order differential equation, turning it into a system of first order linear equations, and find its eigenvalues. I'll have two variables that correspond to the two columns in the matrix. If I swap columns, I end up with two...

Homework Statement This is the second part of a multi-part question. Part (a) shows that: x'' = Ax = \left(\stackrel{-2}{4/3}\stackrel{3/2}{-3}\right)x Part (b): Assume x = \epsilone^{rt} and show that (A - r^{2}I)\epsilon = 0 x is the solution to the second order differential equation...

hi, can some one give me any hints how to solve this problem? thank you i tried to type it here but it dint come up so i uploaded http://tinypic.com/view.php?pic=2hgtqoz&s=3" with the problem. Thank you so much Recall that for an nxn matrix A with distinct eigenvalues \lambda...

I have two problems here; one I think I almost have but I'm stuck, and the other I'm pretty much stumped on.Homework Statement Suppose V is a complex vector space and T is in L(V). Prove that T has an invariant subspace of dimension j for each j = 1, ... dim(V). Homework Equations The Attempt...

I need help starting/doing this proof. Suppose S,T are Linear Operators on a Finite Dimensional Vector Space V. Prove that ST and TS have the same eigenvalues. A linear operator is a linear map from a vector space to itself. thanks.

Homework Statement Define T in L(F3) by T(z1, z2, z3) = (2*z2, 0, 5*z3). Find all eigenvalues and eigenvectors of T.Homework Equations The Attempt at a Solution Well, since we want to find all the eigenvalues, we want the following equation to hold: T(z1, z2, z3) = (2*z2, 0, 5*z3) = \lambda(z1...

Homework Statement Find the eigenvalues and eigenvectors of A = \left(\begin{array}{ccc}5&1&1\\1&3&1\\1&1&3\end{array}\right) The Attempt at a Solution The problem I'm having is finding the eigenvalues for the matrix. In 2d matricies it's not too bad, but in 3d the...

[SOLVED] diagonalization, eigenvectors, eigenvalues Homework Statement Find a nonsingular matrix P such that (P^-1)*A*P is diagonal | 1 2 3 | | 0 1 0 | | 2 1 2 | Homework Equations I am at a loss on how to do this. I've tried finding the eigen values but its getting me...

Homework Statement The task is to show that the eigenvalues of overlap matrix \tilde S are positive. Homework Equations The overlap matrix is defined as (\tilde S)_{nm} = \langle \xi_n \vert \xi_m \rangle , with \xi_k being the base vectors of the wavefunction...

Hi, I'm barely a high school senior who is somewhat overwhelmed by a univ. course. Anyway, we are just learning to solve some basic PDEs using the method of separation of variables. With this method (and the questions we are given) we check three cases to find the eigenvalues of Sturm-Liouville...

Hi, For math we were assigned a subject which we'd present during one class' hour in a group. My group got "Eigenvalues & eigenvectors". So basically first I have to give the definition and explain what it actually is (AX = \lambdaX) and then we can spend the rest of the 45 min on making class...

Question 1 Let A be an nxn matrix such that (A-I)^{2}=O where O is the zero matrix Prove that if {\lambda} is an eigen value of A then {\lambda}=1 My attempt If (A-I)^{2}=O then A=I (1) if {\lambda} is an eigen value of A then Ax={\lambda}x (2) replace (1) in (2) Ix={\lambda}x , but...

Question 1: Proove that if λ is an eigenvalue of [A], then 1/λ is an eigenvalue of [A]{T} Question 2 Proove that a square matrices [A] and [A]T have the same Eigenvalues. Question 3: Show that |det(A)| is the product of the absolute values of the eigenvalues of [A]...

Could some one please explain the logic behind the subroutine tqli(d,e,z) found on pg.1228 of numerical recipes in fortran. For this subroutine, d and e are one dimensional arrays and z is an optional multi-dimensional array(only used if also seeking for eigenvectors of matrix). The 3 modules...

Homework Statement Use direct multiplication to show that for each of the following matrices A, the given vectors v1, v2, and v3 are eigenvectors of A and to find the eigen values lama1, lama2, and lama3 of A: A=top row: (2 -1 3) second row: (-1 6 -1) third row: (3 -5 2)...

Hello Trying to calculate and simulate with Matlab the Steady State Temperature in the circular cylinder I came to the book of Dennis G. Zill Differential Equations with Boundary-Value Problems 4th edition pages 521 and 522 The temperature in the cylinder is given in cylindrical...

How do I determine what the original matrix was that yielded these two eigenvalues with the corresponding eigenvectors: \lambda_1 = -3 Eigenvector: [0,1] \lambda_2 = 2 Eigenvector: [1,0] I've played around with det(A-lambda I) but can't find the matrix! I even just did some trial and...

Q: Prove htat if a matrix U is unitary, then all eigenvalues of U have absolute value 1. My try: Suppose U*=U^-1 (or U*U=I) Let UX=(lambda)X, X nonzero => U*UX=(lambda) U*X => X=(lambda) U*X => ||X||=|lambda| ||U*X|| => |lambda| = ||X|| / ||(U^-1)X|| And now I am really stuck and...

[SOLVED] Complex Numbers: Eigenvalues and Roots Below are some problems I am having trouble with, the computer is telling me my answers are wrong. It may be the way I am inputting the numbers but as my final is in a week and a half I would like to be sure. Thanks,

Hi, Can somebody provide a link(other than numerical recipes) where I can get an optimized 'C' program for calculating eigenvalues of real nonsymmetric martix. Thanks

[SOLVED] Eigenvalues and Eigenspinors Homework Statement (a) Find the eigenvalues and eigenspinors of S_{y}. Homework Equations \hat{Q}f(x) = \lambda f(x) The Attempt at a Solution The above equation wasn't given specifically for this problem; but that's the one I'm trying to...

If I have an operator of the form 1+3\vec{e}\cdot\vec{\sigma} where \vec{e}\cdot\vec{e}=1. How can I find the eigenvalues quickly?

Given an operator \hat{Q} (in the Schrodinger picture) in non-relativistic quantum mechanics and a state |\psi(t)\rangle such that \hat{Q} |\psi(t)\rangle=q(t)|\psi(t)\rangle where q(t) is explicitly time-dependent, can we properly say that |\psi(t)\rangle is an eigenstate of Q with a...

Hi Homework Statement We're given the operators Lx, Ly and Lz in matrix form and asked to show that they have the correct eigenvalues for l=1. Obviously no problem determining the values and Lz comes out right, however we've never actually seen the e.v.s for Lx and Ly. Homework...

Homework Statement I need the eigenvalues and eigenvectors of [[0,0,1][0,2,0][1,0,0]] The Attempt at a Solution How come when I use the determinent method to get the eigenvalues I only end up with 2? Did I make a mistake or is there some other way I'm supposed to find -1, +1?

any ideas on how to go about conducting these please. i will attempt them once i have a clear idea on how to do this. thanks :) let V be the vector space of polynomials over C of degree <= 10 and let "D: V -----> V" be the linear map defined by D(f) = df/dx show (1) D^11=0 (2)...

Problem : in the Attach file

Hey guys, I was wondering what the difference between a generalized eigenspace for an eigenvalue and just an eigenspace is. I know that you can get a vector space using an eigenbasis ie using the eigenvectors to span the space but apart from that I am kinda stumped. Also with regard to...

Homework Statement Let A be the matrix of the linear transformation T. Without writing A, find an eigenvalue of A and describe the eigenspace. T is the transformation on R^3 that rotates points about some line through the origin. Homework Equations maybe...Ax=(lambda)x ? The Attempt...

In standard quantization procedure we should apply commutation rules [p,q]=i. But let's do a simple calculation: i \langle q_0 | q_0 \rangle = \langle q_0 | [p,q] | q_0 \rangle = \langle q_0 | pq | q_0 \rangle - \langle q_0 | qp | q_0 \rangle = q_0 \langle q_0 | p | q_0 \rangle - q_0 \langle...

Q: Suppose the only eigenvalues of A are 1 and -1, and A is similar to a diagonal matrix. Prove that A^-1 = A My Attempt: Suppose the only eigenvalues of A are 1 and -1, and A is similar to a diagonal matrix. =>A is invertible (since 0 is not an eigenvalue of A) and there exists invertible...

This is a MATLAB question. I am trying to find the eigenvalues of a matrix with both real and complex numbers. This is my session. >> A=[1/sqrt(2),i/sqrt(2),0; -1/sqrt(2),i/sqrt(2),0; 0,0,1] A = 0.7071, 0 + 0.7071i, 0 -0.7071, 0 + 0.7071i, 0 0, 0...

We know the eigenvalue relation for the Hamiltonian of a SHO (in QM) though relating the raising and lowering operators we get: H= \hbar \omega (N+1/2) This is true for H=\frac{p^2}{2m}+\frac{m \omega^2 x^2}{2} I would like to solve for another case where V=a\frac{m \omega^2 x^2}{2} where...

I want to prove that if all the eigenvalues of a linear transformation T : V --> V are zero, then T = 0. I think this is obvious but I'm having difficulty putting it into words. If all the eigenvalues of T are zero, then there exists a basis B for V in which [T]_B is the zero matrix. Thus...

Homework Statement I need the eigenvalues of [[3, -1][-1, 1]] (ie [[row1][row2]]) The Attempt at a Solution A-xI = [[3-x, -1][-1, 1-x]] so I get the characteristic polynomial x^2-4x+2=0 from det(A-xI)=0 Is this correct? Because I won't get integer eigenvalues from it

what is a eigen value and eigen function? i have read a lot abt it...i understand the math behind it.. what is its physical significance of it?

This is just a general question: If, when you are calculating the eigenvalues for a matrix, you get a root of 0 (eg. x^3 - x) --> x(x-1)(x+1), what does that mean for the eigenvectors? thanks, w.

In the quantum version of the symmetric infinite well, the energy eigenvalues are, in principle, well-determined. Why would the momentum then have a spread or distribution for a given energy eigenvalue i.e. \phi(p) = 1/(2\pi\hbar) \int_{-a}^{a}dx u_n (x) e^{-ipx/\hbar} where u_n is the...

I have: x' = \left(\begin{array}{cc}2&-5\\1&-2\end{array}\right) x I found that the eigenvalues are r_1 = i and r_2 = - i. Also, I calculated the eigenvectors to be \xi_1 = \left(\begin{array}{c}2 + i\\1\end{array}\right) \xi_2 = \left(\begin{array}{c}2 - i\\1\end{array}\right)...

Homework Statement i'm trying to find the eigenvalues of a matrix and i have the solution but i don't understand how it gets from the step 1 to step 2? could someone please explain. let # = lambda Step 1: (1-#)[(2-#)(-1-#)+1]+[3(-1-#)+2]+4[3-2(2-#)] = 0 Step 2: (1-#)(#+2)(#-3) = 0...

Given a square matrix (arbitrary finite size) where two diagonal entries are 'a' and '-a', what can you derive about the eigenvalues of the matrix? My supervisor mentioned she'd read something about it being provable that the matrix cannot be positive or negative definite. Two of the...

Homework Statement For which real numbers c and d does the matrix have real eigenvalues and three orthogonal eigenvectors? 120 2dc 053 Homework Equations im having trouble getting started on this one. Ive tried using solving for the eigenvalues pretending that c and d are...

Let A be a matrix with real elements. The problem is to estimate eigenvalues of A, real and complex. QR algorithm is fine for real eigenvalues, but obviously fails to converge on complex eigenvalues... So, I'm looking for an alternative that could provide an estimate for complex eigenvalues of...

Homework Statement >M: L_2 -> L_2 > >(Mf)(t) = int(-pi, pi) sin(y-x)f(x) dx > >how do i find eigenvalues/vectors of M and what can i use to find >information about the spectrum? Homework Equations The Attempt at a Solution now i know that sin(y-x) = sinycosx-cosysinx...

I am a second year physics student and have been set a homework assignment to solve a one dimensional time independant schrodinger equation in a finite square well using microsoft excel. I understand the physics behind the situation but am not exactly sure how to use microsoft excel to solve...

Hi I came across a problem of eigenvalues and eigenvectors. It was easy and I solved it but one thing made me unsure about the answer. All the three eigenvectors were zero vectors. Here is the question and my answer: The matrix A= ( -1 0 0 1 0 -2 0 0 0 1 -2 0...

I'm studying for a linear algebra final, and I'm looking over an old final our prof gave us and I've come across something I don't remember ever hearing anything about... Here's the problem: Write down a matrix A for the following condition: A is a 3x3 matrix with lambda=4 with algebraic...

Homework Statement Find all the eigenvalues and eigenvectors of the linear transformation: T(f) = 5f ' -3f T: from C^(nfnty) --> C^(nfnty) where C^(nfnty) is set of continuously functions Homework Equations A scalar B is called an eigenvalue of T if there exists a nonzero element f...

Hi! i want to calculate the eigenvalues and the eigenstates of the momentum operator and the Hamilton operator of a free particle. How do i do this? Thanks for answers!

1. How to show (prove) the Cayley-Hamilton theorem : “Every matrix is a zero of its characteristic polynomial , Pa(A)=0”. 2. A and B are n-square matrices, show that AB and BA have the same eigenvalues. 3. Show that to say that “ 0is an eigenvalue of linear mapping U” is equivalent to “ U...