Eigenvalues Definition and 853 Threads

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

Homework Statement Hi all, I need help with determining the accuracy of finding eigenvalues of defective matrix. The question asks: When a matrix has a defective eigenvalue, the condition number for computing its eigenvalues is infinity. Does this mean that these eigenvalues cannot be...

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...

Let U, T be linear operators on a vector space V. Prove that UT and TU have the same eigenvalues. Any ideas?

Homework Statement A unitary operator U has the property U(U+)=(U+)U=I [where U+ is U dagger and I is the identity operator] Prove that the eigenvalues of a unitary operator are of the form e^i(a) with a being real. NB: I haven't been taught dirac notation yet. Is there a way i can do...

Homework Statement Consider lowering and rising operators that we encountered in the harmonic oscillator problem. 1. Find the eigenvalues and eigenfunctions of the lowering operator. 2. Does the rising operator have normalizable eigenfunctions?Homework Equations a-= 1/sqrt(2hmw) (ip + mwx) a+...

If after you apply an operator and hence calculate the expectation value of a measureable entity and if you get an eigenvalue, then does that mean when you do the measurement, you will always get the same value for that operator entity, each time? I think yes because otherwise what is so...

Weinberg in volume 1 of his QFT text says we do not observe any non-zero eigenvalues of A = J_2 + K_1; B = -J_1 + K_2. He says the "problem" is that any nonzero eigenvalue leads to a continuum of eigenvalues, generated by performing a spatial rotation about the axis that leaves the standard...

In my calc 3 class, we've taken an alternative(?) route to learning maxes and mins of multivariable equations. By using a Hessian Matrix, we're supposed to be able to find the eigenvalues of a function at the point, and determine whether the point is a max, min, saddle point, or indeterminant...

Suppose that B is the inverse of A. Show that if |psi> is an eigenvector of A with eigenvalue a not equal to 0, then |psi> is an eigenvector of B with eigenvalue 1/a. So I know that A|psi> = a|psi>, and I'm trying to prove that A^(-1)|psi> = 1/a|psi>. I tried simplifying A as a 2x2 matrix...

I'm currently researching a 3d tensor, where certain combinations of terms can cause the principal values (eigenvalues) to become complex. This would then seem to imply that the associated eigenvectors would also become complex. What now, if this tensor were part of a larger equation...

Find the Eigenvalues of the matrix and a corresponding eigenvalue. Check that the eigenvectors associated with the distinct eigenvalues are orthogonal. Find an orthogonal matrix that diagonalizes the matrix. (1)\left(\begin{array}{cc}4&-2\\-2&1\end{array}\right) I found my eigenvalues to...

This is how the book introduced eigenvectors: I do not get how the normal vector of x-y = 0 is <1,-1> . Isn't that saying that the x-component is 1 and the y-component is -1? Also how did they get the vector equation <x,y> = t<1,-1> + <a,b> ? Finally, why does \vec{OQ} = \vec{OP}...

If A & B are linear operators, and AY=aY & BY=bY, what is the relationship between A & B such that e^A*e^B=e^(A+B)?? --where e^x=1+x+x^2/2+x^3/3!+...+x^n/n!

If A & B are linear operators, and AY=aY & BY=bY, what is the relationship between A & B such that e^A*e^B=e^(A+B)?? --where e^x=1+x+x^2/2+x^3/3!+...+x^n/n!

Hey all, I have two matrices A,B which commute than I have to show that these eigenvectors provide a unique classification of the eigenvectors of H? From these pairs of eigenvalue is it possible to obtain the eigenvectors? I don't quite know how to procede any suggestions? Thanks...

Hi again, Question: \hat{A} is an Hermitian Operator. If \hat{A}^{2}=2, find the eigenvalues of \hat{A} So We have: \hat{A}\left|\Psi\right\rangle=a\left|\Psi\right\rangle But I actually don't know how to even begin. \hat{A} is a general Hermitian operator, and I don't know where...

If I have two eigenfunctions of an operator with the same eigenvalue how do I construct linear combinations of my eigenfunctions so that they are orhtogonal? My eigenfunctions are: f=e^(x) and g=e^(-x) and the operator is (d)^2/(dx)^2

Find the eigenvalues of the hamiltonian H=a(S_A \cdot S_B+S_B \cdot S_C+S_C \cdot S_D+S_D \cdot S_A) where S_A, S_B, S_C, S_D are spin 1/2 objects _________________________ I rewrite it as H=(1/2)*a*[(S_A+S_B+S_C+S_D)^2-(S_A+S_C)^2-(S_B+S_D)^2] then i define...

Hey, A Hamiltonian has 3 eigenkets with three eigenvalues 1, sqrt(2) and sqrt(3) - will the expectation values of observables in general be period functions of time for this system? I don't know how to procede? Thnaks in advance

Hey guys, I know its possible to diagonalize a matrix that has repeated eigenvalues, but how is it done? Do you simply just have two identical eigenvectors?? Cheers Brent