Eigenvalues for Some Complex In nite Tridiagonal Matrices
Maria Malejki *
AGH University of Science and Technology Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krakow, Poland.
*Author to whom correspondence should be addressed.
Abstract
The discrete spectrum for an unbounded operator J dened by a special innite tridiagonal
complex matrix is approximated by the eigenvalues of its orthogonal truncations. Let σ(J) means
the spectrum of the operator J and
where Limn→∞λn is the set of limit points of the sequence (λn); and the n x n matrix Jn is an
orthogonal truncation of J.
We consider classes of tridiagonal complex matrices for which σ(J) = Λ(J).
Keywords: Tridiagonal matrix, complex Jacobi matrix, discrete spectrum, eigenvalue, asymptotic formula, unbounded operator.