# Eigenvalues

### Some articles on eigenvalues, eigenvalue:

Matrix Differential Equation - Solved Example of A Matrix ODE - First Step
... step, that has already been mentioned above, is finding the eigenvalues ... The process of finding the eigenvalues is not a very difficult process ... Both eigenvalues and eigenvectors are useful in numerous branches of mathematics, including higher engineering mathematics/calculations(i.e ...
Scalar Field Solution - Eigenvalues
... The characteristic polynomial of the Einstein tensor in a minimally coupled massless scalar field solution must have the form In other words, we have a simple eigvalue and a triple eigenvalue, each being the negative of the other ... Multiply out and using Gröbner basis methods, we find that the following three invariants must vanish identically Using Newton's identities, we can rewrite these in terms of the traces of the powers ...
Circular Ensemble - Generalizations
... The eigenvalues of orthogonal matrices come in complex conjugate pairs and, possibly complemented by eigenvalues fixed at +1 or -1 ... For n=2m even and det U=1, there are no fixed eigenvalues and the phases θk have probability distribution with C an unspecified normalization constant ... For n=2m+1 odd there is one fixed eigenvalue σ=det U equal to ±1 ...
SL2(R) - Classification of Elements - Conjugacy Classes
... By Jordan normal form, matrices are classified up to conjugacy (in GL(n,C)) by eigenvalues and nilpotence (concretely, nilpotence means where 1s occur in the Jordan blocks) ... is fixed, and trace and determinant determine eigenvalues), except if the eigenvalues are equal, so ±I and the parabolic elements of trace +2 and ...
Spectral Geometry
... features of the geometry from information about the eigenvalues of the Laplacian ... of a bounded domain in Euclidean space can be determined from the asymptotic behavior of the eigenvalues for the Dirichlet boundary value problem of the Laplace operator ... John Milnor tells us, the information of eigenvalues is not enough to determine the isometry class of a manifold (see isospectral) ...