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.
Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices
We present a lower and an upper bound for the second smallest eigenvalue of Laplacian matrices in terms of the averaged minimal cut of weighted graphs. This is used to obtain an upper bound for the real parts of the non-maximal eigenvalues of irreducible nonnegative matrices. The result can be applied to Markov chains.
Upper bounds for the abscissa of stability of a stable matrix
Upper bounds on the solution of coupled algebraic Riccati equation.
Young's (in)equality for compact operators
If a,b are n × n matrices, T. Ando proved that Young’s inequality is valid for their singular values: if p > 1 and 1/p + 1/q = 1, then for all k. Later, this result was extended to the singular values of a pair of compact operators acting on a Hilbert space by J. Erlijman, D. R. Farenick and R. Zeng. In this paper we prove that if a,b are compact operators, then equality holds in Young’s inequality if and only if .
Дихотомия спектра и критерий устойчивости для секториальных операторов.
Некоторые оценки собственных значений симметричных матриц, отмасштабированных с помощью блочного Якоби
О мероморфных плюс-матрицах-функциях
О спектральных свойствах блочных матриц