Spectrum of a matrix

About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.

Complex time eigenvalues of the one speed neutron transport equation for a homogeneous sphere

Abstract: The time eigenvalue spectrum of the one-speed, isotropic scattering neutron transport equation has been studied for a homogeneous sphere with vacuum boundary conditions. There is a close relationship between the time eigenvalue problem and the criticality problem of the time independent equation for the same model. It is shown that this relation holds even when the time eigenvalues are complex. Using Carlvik's method to solve the criticality problem, it is shown that complex time eigenvalues do actually exist for this model problem. Thus the real eigenvalues found by van Norton(1) do not form the complete spectrum.

A Note on Spectra of Optimal and Superoptimal

Abstract: In this short note, it is proved that given any positive definite Hermitian matrix, the eigenvalues of the superoptimal preconditioned matrix do not exceed the corresponding eigenvalues of the optimal preconditioned matrix.

Recovery of a density from the eigenvalues of a nonhomogeneous membrane

Abstract: The vibrating elastic membrane is a classical problem in Mathematical Physics which arises in a wide variety of physical applications. Since the geometry of the membrane is usually well defined for a particular problem, determination of the nature of any nonhomogeneity is critical. The eigenvalues of particular membranes are often quite accessible experimentally and so a method for the determination of the nonhomogeneity based on the available eigenvalues is of practical importance. Projection of the boundary value problem and its coefficients onto appropriate vector spaces leads to a matrix inverse problem. Although the matrix inverse problem is of nonstandard form, it can be solved by a fix ed-point iterative method. Convergence of the method for a rectangular membrane is discussed and numerical evidence of the success of the method is presented.

Eigenvalues and Whittaker's Function

Abstract: AMONG those who are trying to acquire a general acquaintance with Schrodinger's wave-mechanics there must be many who find their mathematical equipment insufficient to follow his first great problem—to determine the eigenvalues and eigenfunctions for the hydrogen atom. I do not think it is generally realised that Schrodinger's differential equation for this problem is one which is fully treated in a standard text-book, Whittaker and Watson's “Modern Analysis”, Chapter xvi. (I quote from the second edition). It would seem that advantage may be taken of this to make the treatment easier for English readers. I realise that the following is only a slight redressing of Schrodinger's method; but I think it will be intelligible to some who have been unable to appreciate the original, and that it gives a useful idea of the genesis of eigenvalues.