Solving a PDE Eigenvalue Problem: Proving All Eigenvalues Are Positive

ekalbh
Messages
2
Reaction score
0
I have a PDE test next week and I'm kinda confused. How do you prove that eigenvalues are all positive? I know Rayleigh Quotient shows the eigenvalues are greater than or equal to zero, but can someone explain the next step. Thanks in advance
 
Physics news on Phys.org
All eigenvalues are not positive. Are you talking about the eigenvalues of Hermitian operators?
 
Sorry, I mean given a pde, how would you go about finding out if the eigenvalues are positive, negative, zero, or a combination of those.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
View full post »

Similar threads

Eigenvalue problem and initial-value problem?
Replies
2
Views
3K
A Solving an ODE Eigenvalue Problem via the Ritz method
Replies
1
Views
2K
I How can I test for positive semi-definiteness in matrices?
Replies
1
Views
2K
I Solving a Particle on the Surface of a Sphere: Obtaining Eigenvalues
Replies
4
Views
2K
Solving the heat equation with complicated boundary conditions
Replies
9
Views
5K
MATLAB Solving Polynomial Eigenvalue Problem
Replies
2
Views
2K
What Type of PDE is This Modified Diffusion Equation?
Replies
3
Views
2K
I Physics? Setting up PDE for air resistance at high velocity
Replies
2
Views
2K
Quadratic eigenvalue problem and solution (solved in Mathematica)
Replies
2
Views
2K
Showing That the Eigenvalue of a Matrix is 0
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top