1. M


    A permutation matrix of order n is a matrix of size n X n, composed of 0 and 1, that the sum (in the field of real numbers) of elements for each of its columns and each row is equal to 1. Let λ1, λ2, ..., λ5 be the proper numbers of the permutation of the order5. Find λ ∗ = min | λi |...
  2. M

    eigenvalues and eigenvectors

    Hi, I have a problem , Give an example to the T ϵ L(R ^ 4) operator with no real eigenvalues. Please explain
  3. A

    Steady States & Eigenvalues

    For an example problem to solve in an engineering class I was given the following systems and told to find the steady states of each and the eigenvalues for each steady state. 1) dx/dt = x(1-2y-x) dy/dt = y-x 2) x' = x(10-x-y) y' = y(30-2x-y) I know that for steady states I need to...
  4. P

    Eigenvectors and Eigenvalues in relation to a double transformation

    Hi guys, I have the following question: I have been thinking about this for a while now, but I simply cannot work it out... Let V be a linear space of n dimensions over R, and let S,T:V->V be linear transformations. True or False? 1. If v is an eigenvector of S and of T, then v is...
  5. C

    Prove the eigenvalues $\lambda$ of $\lambda \phi_j(x)= \int_G{ K(x-y)\phi_j(y)dy}$ is

    Prove the eigenvalues $\lambda$ of $\lambda \phi_j(x)= \int_G{ K(x-y)\phi_j(y)dy}$ is $\int_G{K(x)\phi_{-j}(x)dx}$, with $\phi_j(x)=(2R)^{-n/2}exp(i\pi j. \frac{x}{R}), j \in \mathbb{Z}^n, x, y \in \mathbb{R}^n, G=\{x \in \mathbb{R}^n: |x_i|\leq R,i=1,...,n\} $ and $K(x)$ is 2R-perodic. When...
  6. A

    Prove U is normal

    I am stuck on this question. Please help. Suppose that V is a finite dimensional inner product space over C and dim V = n; let T be a normal linear transformation of V. If U is a linear transformation of V and T has n distinct eigenvalues such that TU=UT, prove U is normal.(Use spectral...
  7. I

    What is Eigenvalues, Eigenvectors?

    hello what is application of Eigenvalues, Eigenvectors ?
  8. Z

    EigenValues and differential equations.. Please check my math

    Suppose P is the projection matrix onto the 45◦ line y = x in R2. Its eigenvalues are 1 and 0 with eigenvectors (1, 1) and (1,−1). If dy/dt = −Py (notice minus sign) can you find the limit of y(t) at t = ∞ starting from y(0) = (3, 1)? My Solution: dt/dy = -Py, the eigenvalues are now...
  9. A

    Solving for PDE Eigenvalues

    Eigenvalue PDE? How can I solve for lambda of the new problem exactly how the old problem was solved. Both problems are included in the attached picture. Please show steps
  10. C

    Eigenvalues + Eigenvectors

    Suppose X (n × p) is a centered data matrix (i.e. each variable has sample mean zero). Then the sample variance matrix S is given by: (n−1)S = XTX. Suppose λi and ai, i =1,...,p, are the eigenvalues and eigenvectors of XTX. (i) What are the eigenvalues and eigenvectors of S...
  11. W

    Algorithm for eigenvalues and eigenvectors

    Hi! Can someone advise some easy-programmable algorithm that finds eigenvalues and eigenvectors for positively definite (implies symmetric, square) matrix?
  12. L

    Eigenvalues and eigenvectors and diagonalization.

    Let $A$ be an array Diagonalizable and $S$ is a matrix that diagonalizes $A$, i.e. $\[S^{-1}AS=D$ where $D$ is diagonal. Prove that $T$ diagonalizes $A\Leftrightarrow T=CS$ where $AC=CA$. .
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    Can anyone show completely ... Prove that A $A$ and $A^{t}$ have the same eigenvalues.
  14. K

    Eigenvalues and Functions

    Find the eigenvalues and eigenfunctons for y'' + (lambda^2)y = 0 with y(0) = 0 and y(3pi) = 0 Help please, thank you.
  15. M

    For A to have 0 as an eigenvalue, k must be

    Let A= matrix [-7 -8] [-4 k] For A to have 0 as an eigenvalue, k must be? When I did this I thought you would just row reduce and figure out what k would be, but I was wrong. If you could help me, that would be greatly appreciated! Thanks :)
  16. S

    Asymptotic Behavior of Sturm-Liouville eigenvalues

    Hello, I have been stuck on the following problem for a week or so and its killing me. For some context, this is in the section of my book about large eigenvalues, and how to approximate them for Regular Sturm-Liouville differential equations. Consider the equation: \phi'' +...
  17. N

    Eigenvalues of complete partite Graphs.

    The eigenvalues of complete bipartite graph(Km,n) is given by the expression ±√m*n , 0(with multiplicity k-2). Where k is number of nodes in the graph. I am looking for generalization of the expression for eigenvalues of complete n-partite graphs. Does such a expression exists for...
  18. R

    Video: Eigenvalues and eigenvectors made easy

  19. J

    Eigenvalues of piecewise linear systems

    Hi all, I am a theoretical ecology M.Sc student and I'm struggling with the calculation of the eigenvalues of a fairly simple system. I have a difference equations system where the following 3x3 state matrix: line 1:[0, 1-x, 1-x] line 2:[k1, 0, 0] line 3:[0, k2, k3] is valid over x...
  20. A

    Eigenvalues of rotation matrix

    how can it be proved that the eigenvalues of the 2x2 rotation matrix i.e. cos(x) -sin(x) sin(x) cos(x) are cos(x)+isin(x) and cos(x)-isin(x)?