The comparison of spectrum of normalizable matrices
The convergence of a new method for calculating lower bounds to eigenvalues
The -stability problem for real matrices
We give detailed discussion of a procedure for determining the robust -stability of a real matrix. The procedure begins from the Hurwitz stability criterion. The procedure is applied to two numerical examples.
The Eigenvalues and Singular Values of Matrix Sums and Product, VIII: Displacement of Indices
The Gerschgorin discs under unitary similarity
The intersection of the Gerschgorin regions over the unitary similarity orbit of a given matrix is studied. It reduces to the spectrum in some cases: for instance, if the matrix satisfies a quadratic equation, and also for matrices having "large" singular values or diagonal entries. This leads to a number of open questions.
The inertia of Hermitian tridiagonal block matrices.
The Merris index of a graph.
The minimum, diagonal element of a positive matrix
Properties of the minimum diagonal element of a positive matrix are exploited to obtain new bounds on the eigenvalues thus exhibiting a spectral bias along the positive real axis familiar in Perron-Frobenius theory.
The quaternion matrix-valued Young's inequality.
The singularity/nonsingularity problem for matrices satisfying diagonal dominance conditions formulated in terms of directed graphs.
The spectral radii of an operator and its modulus
The structured distance to nearly normal matrices.
Trace inequalities with applications to orthogonal regression and matrix nearness problems.