The convex analysis of unitarily invariant matrix functions.
The critical exponent of operators with constrained spectral radius
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 higher rank numerical range of nonnegative matrices
In this article the rank-k numerical range ∧k (A) of an entrywise nonnegative matrix A is investigated. Extending the notion of elements of maximum modulus in ∧k (A), we examine their location on the complex plane. Further, an application of this theory to ∧k (L(λ)) of a Perron polynomial L(λ) is elaborated via its companion matrix C L.
The norm of the product of a large matrix and a random vector.
The numerical Range of Matrix Polynomials
The optimal perturbation bounds for the weighted Moore-Penrose inverse.
The Perturbation Bounds for Eigenspaces of a Definite Matrix-Pair
The q-numerical range of tridiagonal matrices.
The spectral radii of an operator and its modulus
The Steinitz constant of the plane.
Toeplitz band matrices with exponentially growing condition numbers.
Transient behavior of powers and exponentials of large Toeplitz matrices.
Two applications of a bound on the Hadamard product with a Cauchy matrix.