### Some articles on *eigenvalues, eigenvalue*:

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 ...Spectral Geometry

... identify features of the geometry from information about the

... identify features of the geometry from information about the

**eigenvalues**of the Laplacian ... in Euclidean space can be determined from the asymptotic behavior of the**eigenvalues**for the Dirichlet boundary value problem of the Laplace operator ... However as the example given by John Milnor tells us, the information of**eigenvalues**is not enough to determine the isometry class of a manifold (see isospectral) ...Scalar Field Solution -

... must have the form In other words, we have a simple eigvalue and a triple

**Eigenvalues**... must have the form In other words, we have a simple eigvalue and a triple

**eigenvalue**, each being the negative of the other ...Matrix Differential Equation - Solved Example of A Matrix ODE - First Step

... The first step, that has already been mentioned above, is finding the

... The first 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 ...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 ... since determinant is fixed, and trace and determinant determine**eigenvalues**), except if the**eigenvalues**are equal, so ±I and the parabolic elements of trace +2 and trace 2 ...