### 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

... 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 -

... 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 ...

**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

... 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

... 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

... 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) ...