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...
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...
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...
I have this Hamiltonian --> (http://imgur.com/a/lpxCz)
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...
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...
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...
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...
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...
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}}}...
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...
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?
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...
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?