Read about eigen values | 14 Discussions | Page 1

  1. Mutatis

    Find the eigenvalues and eigenvectors

    Homework Statement Find the eigenvalues and eigenvectors fro the matrix: $$ A=\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} $$. Homework Equations Characteristic polynomial: ## \nabla \left( t \right) = t^2 - tr\left( A \right)t + \left| A \right|## . The Attempt at a Solution I've found...
  2. W

    How are Faces Encoded for Image Recognition?

    Hi all, I think I have an idea of how the Mathematical aspects of Face recognition work. But I am curious as to what an eigenvector would be in this respect. I am trying to understand it through finding out how pixels are encoded: What map takes a pixel into a collection of...
  3. F

    Linear algebra matrix to compute series

    Post moved by moderator, so missing the homework template. series ##{a_n}## is define by ##a_1=1 ## , ##a_2=5 ## , ##a_3=1 ##, ##a_{n+3}=a_{n+2}+4a_{n+1}-4a_n ## ( ##n \geq 1 ##). $$\begin{pmatrix}a_{n+3} \\ a_{n+2} \\ a_{n+1} \\ \end{pmatrix}=B\begin{pmatrix}a_{n+2} \\ a_{n+1} \\ a_{n} \\...
  4. referframe

    I Eigenvectors - eigenvalues mappings in QM

    In non-relativistic QM, say we are given some observable M and some wave function Ψ. For each unique eigenvalue of M there is at least one corresponding eigenvector. Actually, there can be a multiple (subspace) eigenvectors corresponding to the one eigenvalue. But if we are given a set of...
  5. B

    I How do i find the eigenvalues of this tough Hamiltonian?

    I have this Hamiltonian --> ( Where each G is a matrix. I want to find the eigenvalues but I'm getting hung up on the fact that there are 6 indices. Each G matrix lives in a different space so I can't just multiply the G matrices together. If I built this Hamiltonain...
  6. Adgorn

    I Regarding the linear dependence of eigenvectors

    Let's say we have a set of eigenvectors of a certain n-square matrix. I understand why the vectors are linearly independent if each vector belongs to a distinct eigenvalue. However the set is comprised of subsets of vectors, where the vectors of each subset belong to the same eigenvalue. For...
  7. F

    I Third Invariant expressed with Cayley-Hamilton Theorem

    The Cayley-Hamilton Theorem can be used to express the third invariant of the characteristic polynomial obtained from the non-trivial solution of the Eigenvector/Eigenvalue problem. I follow the proof (in Chaves – Notes on Continuum Mechanics) down to the following equation, then get stuck at...
  8. G

    Sum of eigenvectors of linear transformation

    Homework Statement Find all values a\in\mathbb{R} such that vector space V=P_2(x) is the sum of eigenvectors of linear transformation L: V\rightarrow V defined as L(u)(x)=(4+x)u(0)+(x-2)u'(x)+(1+3x+ax^2)u''(x). P_2(x) is the space of polynomials of order 2. Homework Equations -Eigenvalues and...
  9. Samuel Williams

    Eigenvalue and eigenvectors, bra-ket

    Question Consider the matrix $$ \left[ \matrix { 0&0&-1+i \\ 0&3&0 \\ -1-i&0&0 } \right] $$ (a) Find the eigenvalues and normalized eigenvectors of A. Denote the eigenvectors of A by |a1>, |a2>, |a3>. Any degenerate eigenvalues? (b) Show that the eigenvectors |a1>, |a2>, |a3> form an...
  10. D

    Diagonal Scaling of a 2x2 Positive Definite Matrix

    Given a Positive Definite Matrix ## A \in {\mathbb{R}}^{2 \times 2} ## given by: $$ A = \begin{bmatrix} {A}_{11} & {A}_{12} \\ {A}_{12} & {A}_{22} \end{bmatrix} $$ And a Matrix ## B ## Given by: $$ B = \begin{bmatrix} \frac{1}{\sqrt{{A}_{11}}} & 0 \\ 0 & \frac{1}{\sqrt{{A}_{22}}}...
  11. Diffie Heltrix

    Norm indueced by a matrix with eigenvalues bigger than 1

    Suppose we pick a matrix M\in M_n(ℝ) s.t. all its eigenvalues are strictly bigger than 1. In the question here the user said it induces some norm (|||⋅|||) which "expands" vector in sense that exists constant c∈ℝ s.t. ∀x∈ℝ^n |||Ax||| ≥ |||x||| . I still cannot understand why it's correct. How...
  12. H

    Eigenvalues and Eigenvectors

    What does it mean when it says eigenvalues of Matrix (3x3) A are the square roots of the eigenvalues of Matrix (3x3) B and the eigenvectors are the same for A and B?
  13. Thor90

    Finding eigenvalues with QR method

    Hi, I am trying to solve the problem of finding eigenvalus for a general square symmetric matrix with the QR algorithm. I have understood that this task is much easier if the matrix is in an Hessemberg form, so I have implemented a function that does that with the Housholder method, but I can't...
  14. K

    Physical significance of Eigenvalues and Eigenvector?

    I want to know what exactly Eigen value imply. What is its Physical significance ? Physical significance of eigen vector? Does eigen value concept apply in signal processing or evalvating frequency response off a system?