On the norm of GCD and related matrices.
On the lower bound of the spectral norm of symmetric random matrices with independent entries.
On the matrix norm subordinate to the Hölder norm.
On the orbit of the centralizer of a matrix
Let A be a complex n × n matrix. Let A' be its commutant in Mₙ(ℂ), and C(A) be its centralizer in GL(n,ℂ). Consider the standard C(A)-action on ℂⁿ. We describe the C(A)-orbits via invariant subspaces of A'. For example, we count the number of C(A)-orbits as well as that of invariant subspaces of A'.
On the polynomial numerical hull of a normal matrix.
On the relation between the numerical range and the joint numerical range of matrix polynomials.
On the shortest lattice vectors in a three-dimensional translational (Bravais) lattice
On the spectral norm of a random Toeplitz matrix.
On tropical Kleene star matrices and alcoved polytopes
In this paper we give a short, elementary proof of a known result in tropical mathematics, by which the convexity of the column span of a zero-diagonal real matrix is characterized by being a Kleene star. We give applications to alcoved polytopes, using normal idempotent matrices (which form a subclass of Kleene stars). For a normal matrix we define a norm and show that this is the radius of a hyperplane section of its tropical span.
On two characteristic properties of Euclidean norms.
Operator inequalities of Jensen type
We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if f : [0;1) → ℝ is a continuous convex function with f(0) ≤ 0, then [...] for all operators Ci such that [...] (i=1 , ... , n) for some scalar M ≥ 0, where [...] and [...]
Operator norms of words formed from positive-definite matrices.