Cauchy's interlace theorem and lower bounds for the spectral radius.
Changes in signature induced by the Lyapunov mapping .
Comparison theorems for weak nonnegative splittings of -monotone matrices.
Concentration of the spectral measure for large random matrices with stable entries.
Concentration of the spectral measure of large Wishart matrices with dependent entries.
Convergence of -norms of a matrix
a recurrence relation for computing the -norms of an Hermitian matrix is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the -norms for the approximation of the spectral radius of an Hermitian matrix an a priori and a posteriori bounds for the error are obtained. Some properties of the a posteriori bound are discussed.
Convex -invariant functions and refinements of von Neumann’s inequality
A function on which is -invariant is convex if and only if its restriction to the subspace of diagonal matrices is convex. This results from Von Neumann type inequalities and appeals, in the case where , to the notion of signed singular value.
Cyclic products and an inequality for determinants