Eigenvector Definition and 144 Threads

Homework Statement A = 2 -2 -2 5 Eigenvalues are: 6, 1 Find eigenvectors. My only question is about order. My book lists them in the opposite order as I and I am not sure where I went wrong. Homework Equations A = 2 -2 -2 5 Eigenvalues are: 6, 1 The Attempt at a...

Hello, My question is this. Is it possible to prove that there exist an eigenvectors for a symmetric matrix without discussing about what eigenvalues are and going into details with characteristic equations, determinants, and so on? This my short proof for that: (The only assumption is ##A##...

Hello. I am working on a project with a double pendulum and I am currently looking for the normal mode frequencies. I don't think that's too important to answer my question, but in the derivation I hit a point that look like this:(K-M\omega^{2})\alpha=0. Here, K and M are 2x2 square matrices. I...

Homework Statement ##A=\begin{bmatrix} 16 &{-6}\\39 &{-14} \end{bmatrix}## Homework Equations The Attempt at a Solution I did ##A=\begin{bmatrix} 16-\lambda &{-6}\\39 &{-14-\lambda} \end{bmatrix}## and got that ##\lambda_1=1+3i## and ##\lambda_2=1-3i## The solution...

My friends and I have been struggling with the following problem, and don't understand how to do it. We have gotten several different answers, but none of them make sense. Can you help us? **Problem statement:** Let $V$ be the vector space of real-coefficient polynomials of degree at most $3$...

Homework Statement I was doing this practice exam and I had to calculate the eigenvalues en vectors. The matrix had two eigenvalues, I calculated one eigenvector. But when I was performing row operations for the second eigenvector, the matrix with the second eigenvalue substitued became an...

Hello MHB, Solve the following system of linear differential equation $$f'=f-g$$ $$g'=f+g$$ with bounded limit $$f(0)=0$$, $$g(0)=1$$ could anyone check if My answer is correct? Just to make sure I understand correctly! ps we get $$\lambda=1-i$$ and $$\lambda=1+i$$ Regards, $$|\pi\rangle$$

Hello MHB, solve this system of linear differential equation $$f'=f-g-h$$ $$g'=-f+g-h$$ $$h'=-f+g+h$$ with boundary conditions $$f(0)=1$$, $$g(0)=2$$ and $$h(0)=0$$ we get that $$\lambda=1$$ and $$\lambda=0$$ now for eigenvector or we can call it basis for eigenvector $$\lambda=0$$ i get Is...

Hi everyone, :) This is one of those questions I encountered when trying to do a problem. I know that a eigenvector of a linear transformation should be non-zero by definition. So does that mean every linear transformation has eigenvectors? What if there's some linear transformation where no...

A=a.a', where a is an N by 1 vector,a'a=5,and T is transpose. a)Give the largest eigenvalue of A. b)what is the corresponding eigenvector? Please help me to solve the problem.

Well, I know this have no sense. But I was trying to solve a problem on Cohen Tannoudji. The problem is in chapter IV, complement ##J_{IV}##, exercise 8. It says: Consider an electron of a linear triatomic molecule formed by three equidistant atoms. We use ##\left | {\phi_A} \right >, \left |...

Hi everyone, I'm currently working my way through Dirac's Quantum Mechanics, and I found this proof really irritating. We're trying to demonstrate that any eigenket can be expressed as a sum of eigenkets of a real linear function \xi which satisfies the equation \varphi(\xi) =...

An eigenvector is defined as a non-zero vector 'v' such that A.v = λ.v I don't understand the motive behind this. We are trying to find a vector that when multiplied by a given square matrix preserves the direction of the vector. Shouldn't the motive be the opposite i.e. finding the matrix...

Homework Statement Let B be the linear operator (1-x^{2}) \frac{d^2}{dx^2}-x\frac{d}{dx} Show that T_{4}(x) = 8x^{4} - 8x^{2} + 1 is an eigenvector of B, and find the corresponding eigenvalue. Attempt Righto, I find these rather difficult so a step by step solution would be nice but...

Quick question on eigenvectors; Are there any general properties of a matrix that guarantee that a zero will or will not appear as an element in an eigenvector? Thank you!

Hi, A - I =\begin{bmatrix} -0.5253 & 0.8593 & -0.1906 \\ -0.8612 & -0.5018 & 0.1010 \\ 0.1817 & 0.1161 & -0.0236\end{bmatrix} My eigenvector answer is t= k(−0.0137,0.225,1) My solution sheet's answer is t = k(-0.0088, 0.216, 1) Could I please ask that somebody checks this by...

Homework Statement True/False: If true give a proof, if false give a counterexample. a) If A and B have the same eigenvector X, then A+B should also have the same eigenvector, X. b) if A has an eigenvalue of 2, and B has an eigenvalue of 5, then 7 is an eigenvalue of A+B...

Here is the question: Here is a link to the question: Find the eigenvector? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hi, I'm trying to find an eigenvector of a matrix. I know that λ = 1, so my matrix (A - λI) is [-0.5253, 0.8593, -0.1906; -0.8612, -0.5018, 0.1010; 0.1817, 0.1161, -0.0236] And from rows 2 and 3 I get these simultaneous equations -0.8612t_{1}-0.5018t_{2}+0.1010t_{3}=0...

Homework Statement Homework Equations The Attempt at a Solution I don't know what's wrong with my work. I can't obtain the eigenvector provided in the model answer. [SIZE="5"]My work [SIZE="5"] Model Answer

Homework Statement Let W be a 1-dimensional subspace of V that is A-invariant. Show that every non zero vector in W is a eigenvector of A. [A element of Mn(F)] The Attempt at a Solution We know W is A-invariant therefore for all w in W A.w is in W. W is one dimensional which implies to...

[0 1] [-2 -2] This is the 2x2 matrix. [λ -1] [2 λ+2] This is the matrix that equals λI - A. Here are the eigenvalues I found: λ = -1 + i, -1 - i I am really confused at what to do next to find the eigenvectors. I keep looking online for help but I still can't figure it...

any1 can please tell me the eigen vector for following matrix: [0 0 a 0 0 0 0 0 0] please elaborate ur answer!

Homework Statement Write the eigenvector of \sigmax with +1 eigenvalue as a linear combination of the eigenvectors of M. Homework Equations \sigmax = (0,1),(1,0) (these are the columns) The Attempt at a Solution ... Don't know what to do. Can someone show me how to do this using...

Hey guys, I've been trying to brush up on my linear algebra and ran into this bit of confusion. I just went through a proof that an operator with distinct eigenvalues forms a basis of linearly independent eigenvectors. But the proof relied on a one to one mapping of eigenvalues to...

Homework Statement I'm doing an ODE for homework and I can't find the eigenvector for this matrix (sorry, I don't know how to make matrices on here. Consider these as one matrix.): [ 2 0] [v_{1}] = [0] [ 1 1] [v_{2}] = [0] Homework Equations The only way he has taught us...

Homework Statement A=||A(i,j)|| (i,j=1,…,n) (n>2) is a binary matrix with zero diagonal and A(i,j)=1-A(j,i) for i≠j. W=(1,1,…,1)’ is an eigenvector for matrix B=A*A. Will W be an eigenvector for matrix A too? Why? 2. The attempt at a solution Let have a look at these two statements: "a"...

Hello people! I am having a bit trouble with verifying my result when i compute the eigenvectors for the following matrix: A=[[3,4],[3,2]] I know for sure that the eigenvalues is respectively -1 and 6, so i start finding a solution for the following null spaces: 1)...

So I'm a bit confused between these two and can't quite find any useful resources online. So is an eigenspace a special type of eigenvector cause that's how I understand it now.

Homework Statement This problem will guide you through the steps to obtain a numerical approximation of the eigenvalues, and eigenvectors of A using an example. We will define two sequences of vectors{vk} and {uk} (a) Choose any vector u \in R2 as u0 (b) Once uk has been determined, the...

for the matrix {5,0} {2,-2} when determining the eigenvector for its 2nd eigenvalue, -2, you would start out by doing {5--2 ,0} {2 ,-2--2} giving {7,0} {2,0} In equation form this is 7u + 0v = 0 2u + 0v = 0 Ordinarily I would set u or v to a value and solve...

Hi, So for some reason I have the hardest time trying to work with polynomials in linear algebra. I can't explain it, but whenever I see a question I draw a complete blank. Question: i) Find all the eigenvalues. ii) for each eigenvalue λ, find a basis of the eigenspace Eλ. T: P3(R) -->...

Homework Statement I've started off with a 2x2 matrix of (0) (i) (-i) (0) and I found the eigenvalues to be +1, -1 Then I found the resulting 2x1 eigenvectors to be (-i) (1) and (1) (-i) I now need the normalised eigenvectors. Homework Equations The...

In my lecture notes my prof used the eigenvalue c= 1 + i and ended up with the matrix with (5 3+i) as row 1, and the second row is zeroes. After that, he simply wrote that the basis for this eigenvalue c is (3+i,-5) (in column form) without explaining. How did he get that basis? I tried working...

A = [0 0] [1 -3] (2 x 2 matrix, bad formatting) I need to find the eigenvector for lambda1 and lambda2. I figured out lambda1 = 0 and lambda2 = -3. For lambda1 the eigenvector works fine, but for lambda2 I get it as v = (0,0), which is not possible. Any ideas?

Homework Statement lets say i have a matrix A which is symmetric i diagonalize it , to P-1AP = D Question 1) am i right to say that the principal axis of D are no longer cartesian as per matrix A, but rather, they are now the basis made up of the eigen vectors of A? , which are the columns...

Homework Statement Find the characteristic equations, eigenvalues and eigenvector of the following matrix Homework Equations The Attempt at a Solution Somehow somewhere I think the solution is wrong, based on online Eigenvector calculator on the web. Please do provide me actual answers and...

1.Hello! I am having trouble understanding what A.M. is in the problem which asks, "Find the eigenvalues and eigenvectors associated with the matrix and find the a.m and g.m of each; for example... -1 0 0 1 0 1 - I * Lambda 0 2 1 The Attempt at a...

Homework Statement Find the Eigenvector of the matrix.Homework Equations Ax=λx A= [2 0 1] [0 3 4] [0 0 1]The Attempt at a Solution Ok I'm just having a major brain fart here, been doing this all day. For λ=2, I solved for x and get this solution, [0 1 0][x1] [0] [0 0 1][x2]=[0] [0 0...

Homework Statement Find the eigenvalues and the eigenvectors for the given matrix.Homework Equations \[ A = \left[ {\begin{array}{ccc} -1 & 6 & 2 \\ 0 & 5 & -6 \\ 1 & 0 & -2 \\ \end{array} } \right] \]The Attempt at a Solution I solved A-\lambda I = 0 and got eigenvalues of -4 and 3...

I have the following complex eigenvector: -1+2i -5 0 1 1+2i 0 What is the best way to go about solving these problems? I've done a few by inspection/trial&error, but I believe there has to be a more formal way to do it.

Homework Statement For reference: Problem 1.8.5 parts (3) , R. Shankar, Principles of Quantum Mechanics. Given array \Omega , compute the eigenvalues ( e^i^\theta and e^-^i^\theta ). Then (3) compute the eigenvectors and show that they are orthogonal. Homework Equations Eulers...

Homework Statement For a material the stress is defined by the means of the stress matrix O O = (6 1 -2 1 2 2 -2 2 5) Expressed in MPA It can be derived that the principe stress are: O1= 4-sqrt(13), O2= 5 and O3=4+sqrt(13) I know you can derive the principal...

Homework Statement This is a general question... I can easily go from a matrix A to its eigenvalues and then eigenvectors but how would I go from the eigenvalues and eigenvectors to a feasible original matrix? Any thoughts appreciated!

I can do everything, until I get to the point of actually putting the system of equations into that eigenvector "form". I won't use my actual numbers, but say I have solved everything and got: ax = by ax = by Where a and b are 2 numbers, but a doesn't equal b. Does this mean that for everyone...

Homework Statement \begin{bmatrix} -7 && -16 && 4\\ 6 && 13 && -2\\ 12 && 16 && 1 \end{bmatrix} Diagonalize the matrix (if possible), given that one eigenvalue is 5, and that one eigenvector is {-2, 1, 2}Homework Equations A=PDP^{-1} The Attempt at a Solution If I were allowed to simply...

Homework Statement Let A = matrix [a b] row 1 [c d] row 2 (2x2 matrix) with a>0, b>0,c>0,d>0. Show that A has an eigenvector [x,y] (2x1) with x>0, y>0 Homework Equations The Attempt at a Solution I've tried finding the characteristic polynomial by using det((lambda)I - A)...

Homework Statement Show that, for all complexe numbers \alpha, a has a unique eigenvector |\alpha\rangle that is nothing else but the coherent state \psi(x)=\frac{e^{-\frac{i}{2\hbar}\langle X\rangle\langle P\rangle}}{(\pi\ell^2)^{1/4}}e^{-\frac{(X-\langle...

Homework Statement I can calculate the proper eigenvalues, but when I plug them back into the matrix, I get x1=0 and x2=0. But this is not the answer Maple gives me! How do I solve for the eigenvector when it appears that a zero vector is the only solution? Homework Equations For...

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.