Eigenvalues Definition and 820 Threads

Can someone explain these to me?

Hi all, Here is this problem that I have been at for some time now: find eigenvalues and corresponding eigenvectors of the following linear mapping on a vector space of real 2 by 2 matrices: L(X) = AX - XA, where A is 2 by 2 symmetric matrix that is not a scalar multiple of identity...

Homework Statement When trying to solve a question about parameter independence of certain aspects of the Jacobian of a real valued function on a manifold I came to the point where I have to show the following: Let A be a matrix, J be the Jacobian of an orthogonal transformation (I suppose we...

I'm trying to find the Eigenvectors and eigenvalues of this matrix: [ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 ] I get 0, 1, and -1 as my eigenvalues. Starting with 0, I solve for reduced row echelon form and get the matrix: [ 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ] My question is, and maybe my...

Homework Statement I attached the problem in a picture so its easier to see. Homework Equations The Attempt at a Solution These are the values i got \lambda_ 1 = 1 \lambda_ 2 = -1 x_1 = [-i; 1] (x_1)^H = [i 1] x_2 = [ i; 1] (x_2)^H = [-i 1] * where x_1 and x_2 are...

Find the characteristic polynomial, eigenvectors, and eigenvalues of the matrix. [ 2 -2 3 0 3 -2 0 -1 2 ] My characteristic poly is x^3 - 7x^2 + 14x - 8 The roots are 1, 2, and 4. When solving the system, (2I - A)x = 0 I get: [ 0 1 0 0 0 0 1 0 0 0 0 0 ] Can...

Homework Statement in seeking of eigenvalues and eigenvectors of a given matrix A, is it permissible first to simplify A by means of some elementary operation? (that is, are the eigenvalues and eigenvector of A invariant with respect to elementary row operation)? (prove it)Homework Equations...

how does one systematically find the eigenvectors of a 2x2 (or higher) Real matrix given complex eigenvalues?

Homework Statement consider the system x' = \left[-1 & -1\\ -.5 & -1\right]x (I'm sorry I can't seem to get a new row in! the second line is [-.5 -1] solve the system. What are the eigenvalues of the coefficient matrix? Classify the equilibrium point at the origin as to type...

Hello, I use Arnoldi iterative algorithm in order to compute the eigenvalues of a matrix. I know that the eigenvalues are of the form \lambda(1+j/c) and I can totally estimate them. The problem that occurs is that both the range of \lambda_0 and c is for example [100,1000]. That means that there...

[FONT="Georgia"]I'm trying to compute the eigenvalues for a 32x32 symbolic matrix (with one variable) in Mathematica. I get the following error: [SIZE="1"][SIZE="3"]Eigenvalues::eival: Unable to find all roots of the characteristic \ polynomial. >> [FONT="Georgia"]What could be a possible...

What determines whether an operator has discrete or continuous eigenvalues? Energy and momentum sometimes have discrete eigenvalues, sometimes continuous. Position is always continuous (isnt it?) Spin is always discrete (isn't it?) Why?

Homework Statement T: R3[x] R3[x] // for some reason the arrow symbol isn't working! When I do the arrow it previews as the third power for some reason. Also, whenever I preview post, it adds [b]1 [b]2 b[3] again for some reason and I have to delete those lines every time...a bit fustrating...

hello, two quick question here. I've got the answer correct (I think), but I am not too sure how to explain it in words. So I hope someone tell me is my attempted explanation correct. 1) what is the maximum of non-zero eigenvalues a singular square matrix with 7 rows can have? up to...

Homework Statement Find the eigenvalues and eigenvectors for the matrix [{13,5},{2,4}] Homework Equations None The Attempt at a Solution Well eigenvalues is easy, and turn out to be 14 and 3. So using eigenvalue 3, the two equations 10x1 + 5x2=0 and 2x1 + x2=0. Using these, I assumed...

Homework Statement The https://www.physicsforums.com/showthread.php?t=403476" was to determine the eigenvalues of the following matrix. The problem of interest deals with actually finding a solution to the system above without the use of matrix methods. Homework Equations The...

Homework Statement The Attempt at a Solution I haven't tackled anything bigger than a 3x3 matrix. Anyone have any good pointers for reducing this matrix? I'm assuming the quickest way is still going to be the cofactor method?

urgent help!.. Finding eigenvalues of angular momentum operators the question is asking to find the eigenvalues of: 3/5 Lx - 4/5 Ly ... I feel that i have to connect it with the L^2 and Lz operators but i just have no idea how to start .. any suggestions will be greatly appreciated ..

Can zero be a distinct eigernvalue?

Homework Statement I put a triangle around the problem of interest. Homework Equations The Attempt at a Solution I solved for the eigenvalues, resulting in double-zero values. My question is, using the variation of parameters method, which is what (14) refers to in the...

My lecturer keeps telling me that if a density matrix describes a pure state then it must contain only one non-zero eigenvalue which is equal to one. However I can't see how this is true, particularly as I have seen a matrix \rho_A = \begin{pmatrix} 1/2 & - 1/2 \\ -1/2 & 1/2 \\ \end{pmatrix} for...

Homework Statement I have a matrix H= [h g g h] and I need to find the eigenvalues and normalised eigenvectors Homework Equations The Attempt at a Solution I subtracted lamda from the diagonal and then solved for the determinant equally zero. The eigenvalues I found were...

Homework Statement Homework Equations Conjugate of a complex number Matrix reductionThe Attempt at a Solution My attempt is bordered. Sorry about the quality. So I'm not sure what I'm missing. I use the exact same method that I use for normal eigenvectors, just with complex numbers in the mix.

Homework Statement Find the general solution of the given system. The given matrix is X' = (1st row (1,-1,2) 2nd row (-1,1,0) 3rd row (-1,0,1))X 2. The attempt at a solution The eigenvalue determinant = (1st row (1-λ,-1,2) second row (-1,1-λ,0) 3rd row (-1,0,1-λ) Solving the...

Homework Statement I'll give an example. Ex: x'=[-1/2 1; -1 -1/2]x. Homework Equations Assume a solution of the form x=$ert for these type of problems. Euler's formula: ebi = cosb + isinb The Attempt at a Solution |A-rI|=0 ---> r= -1/2 +/- i ---> x= e-t/2 ( C1(cost...

Use the trace and determinant to compute eigenvalues. I know how to do this with a 2x2 but not sure how to do it with a matrix of nxn where n>2. \begin{bmatrix} \frac{1}{2} & \frac{1}{3} & \frac{1}{5}\\ \frac{1}{4} & \frac{1}{3} & \frac{2}{5}\\ \frac{1}{4} & \frac{1}{3} & \frac{2}{5}...

Homework Statement Prove all eigenvalues = 1 or -1 when A is circulant and satisfying A=A^T=A^-1 I can think of an example, the identity matrix, but i can't think of a general case or how to set up a general case. Homework Equations The Attempt at a Solution I can only show by...

This problem, and all the others on this homework assignment, are making me angry. Homework Statement Find the general solution of the system of equations. ... x'=[-3 5/2; -5/2 2]x Homework Equations Just watch me solve The Attempt at a Solution Assume there's a...

Hi, I am having a lot of difficulty conceptually understanding what eigenfunctions and eigenvalues actually are, their physical meaning, i.e. what they represent, and how they interact. Would anybody happen to be able to explain them in relatively simple terms? I didn't know whether to put...

Homework Statement This isn't really a question in particular. I am doing my first Differential Equations course, and in the complex eigenvalues part, I am getting confused as to how to find the eigenvectors. Example: Solve for the general solution of: x' = (1 -1)x (don't know how to...

I need to compute the 3 eigenvalues and 3 eigenvectors of a symmetric 3x3 matrix, namely a stress tensor, computationaly (in C++). More specific details http://en.wikipedia.org/wiki/Principal_stress#Principal_stresses_and_stress_invariants". Basically 2 questions: 1. I am running into trouble...

If v is an eigenvector of an invertible matrix A, which of the following is/are necessarily true? (1) v is also an eigenvector of 2A (2) v is also an eigenvector of A^2 (3) v is also an eigenvector of A^-1 A) 1 only B) 2 only C) 3 only D) 1 and 3 only E) 1,2 and 3 I am pretty sure...

Let C be a 2 × 2 matrix such that x is an eigenvalue of C with multiplicity two and dimNul(C − xI) = 1. Prove that C = P |x 1|P^−1 |0 x| for some invertible 2 × 2 matrix P. I'm not sure where to start EDIT |x 1| |0 x| is the matrix I don't know why it's...

Hey guys, I'm studing to my exams now, and I came accors this question i eigenvectors where you find them and bla bla. There is part to it which asks to express vetor X= [2/1] as a linear combination of eigenvectors. Hence calculate B2X, B3X, B4X and B51X, simplifying your answers as...

Homework Statement I'm given a standard form of Bessel's equation, namely x^2y\prime\prime + xy\prime + (\lambda x^2-\nu^2)y = 0 with \nu = \frac{1}{3} and \lambda some unknown constant, and asked to find its eigenvalues and eigenfunctions. The initial conditions are y(0)=0 and...

Hi guys I have an analytical expression f(x) for my density of states, and I have plottet this. Now, I also have a complete list of my Hamiltonians eigenvalues. When I make a histogram of these eigenvalues, I thought that I should get an exact (non-continuous) copy of my plot of f(x). They...

So I have a couple of questions in regards to linear operators and their eigenvalues and how it relates to their matrices with respect to some basis. For example, I want to show that given a linear operator T such that T(x_1,x_2,x_3) = (3x_3, 2x_2, x_1) then T can be represented by a diagonal...

Homework Statement Please see the attached image. The first line just finds the eigenvalues of that matrix. The second line finds the eigenvectors. The third line just takes row 1 and row 3 of that matrix and find the determinant. The fourth line just takes row 2 and row 4 of that...

Hey, I'm wondering if I have a known set of eigenvalues (-1, +1, 0) for A, if I can prove that the matrix A = A3? I can prove that if A3 = A, that the eigenvalues would be −1, +1, and 0. The following is the proof: A*k=lambda*k A3*k=lambda3*k Since A=A3, A*k=A3*k lambda*k=lambda3*k...

Homework Statement f is an endomorphism of Rn[X] f(P)(X)=((aX+b)P)' eigenvalues of f? Homework Equations (a,b)<>(0,0) The Attempt at a Solution If a=0, then f(P)=bP', and only P=constant is solution if a<>0, then I put Q=(ax+b)P, f(P)=cP is equivalent to (ax+b)Q'=Q (E)...

Homework Statement T: V-> V, dimV = n, satisfies the condition that T2 = T 1. Show that if v \in V \ {0} then v \in kerT or Tv is an eigenvector for eigenvalue 1. 2. Show that T is diagonalisable. Homework Equations The Attempt at a Solution I have shown in an earlier part...

Homework Statement Let V be the space of polynomials with degree \leq n (dimV=n+1) i. Let D:V->V be differentiation, i.e. D: f(x) -> f'(x) What are the eigenvalues of D? Is D diagonalisable? ii. Let T be the endomorphism T:f(x) -> (1-x)2 f''(x). What are the eigenvalues of T? Is...

Oh it gives me headache... been thinking on this problem for a while, and don't even know where to begin! Could anyone give me a hint at least?? :( Problem: Let A be (3x3) matrix : [ 4 -2 2; 2 4 -4; 1 1 0] and u (vector) = [1 3 2]. a) Verify that Au = 2u I got this one without a problem...

Homework Statement T(f(x)) = 5 f(x) T is defined on C. Find all real eigenvalues and real eigenfunction. V:R -> R Homework Equations Not sure. The Attempt at a Solution No, clue. I can find eigenvalues for matrices, that's not a problem. I'm having problem that its a T(function) =...

Homework Statement What are the eigenvalues and eigenvectors of the momentum current density dyadic \overleftrightarrow{T} (Maxwell tensor)? Then make use of these eigenvalues in finding the determinant of \overleftrightarrow{T} and the trace of \overleftrightarrow{T}^2 Homework...

Hello, Let's say I have a 2x2 matrix,we call it A with the eigenvalues +1 , -1. Now I let's define that m=m0*A. (m0 is const). Are the eigenvalues become +m0 and -m0? If so why?

Homework Statement Show that lambda = 1 is an eigenvalue of the matrix 2,-1, 6 3,-3, 27 1,-1, 7 and find the eigenvalues and the corresponding eigenvectors Homework Equations The Attempt at a Solution I don't understand how to actually get eigenvalues and...

Homework Statement Hello and thanks again to anyone who has replied my posts. Your help is a great deal and really appreciated. I have the following homework question which I have answered and I want a comment if it is valid or illogical: We are given a matrix, with eigenvalues 3 and...

Homework Statement If A is nonsingular, prove that the eigenvalues of A-1 are the reciprocals of the eigenvalues of A. *Use the idea of similar matrices to prove this. Homework Equations det(I\lambda - A) = 0 B = C-1AC (B and A are similar, and thus have the same determinants) The...

Let A be a matrix corresponding to projection in 2 dimensions onto the line generated by a vector v. A) lambda = −1 is an eigenvalue for A B) The vector v is an eigenvector for A corresponding to the eigenvalue lambda = −1. C) lambda = 0 is an eigenvalue for A D) Any vector w perpendicular to...