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.
Perturbations of functions of diagonalizable matrices.
Polynomial numerical hulls of order 3.
Polynomials of the eigenvalues and powers of matrices
Positive definiteness of tridiagonal matrices via the numerical range.
Product of operators and numerical range preserving maps
Let V be the C*-algebra B(H) of bounded linear operators acting on the Hilbert space H, or the Jordan algebra S(H) of self-adjoint operators in B(H). For a fixed sequence (i₁, ..., iₘ) with i₁, ..., iₘ ∈ 1, ..., k, define a product of by . This includes the usual product and the Jordan triple product A*B = ABA as special cases. Denote the numerical range of A ∈ V by W(A) = (Ax,x): x ∈ H, (x,x) = 1. If there is a unitary operator U and a scalar μ satisfying such that ϕ: V → V has the form A...
Quadratische Identitäten bei Polygonen.
Remark to a problem on 0-1 matrices
Reverse rearrangement inequalities via matrix technics.
Reverses of the Golden-Thompson type inequalities due to Ando-Hiai-Petz.
Schatten norms of Toeplitz matrices with Fisher--Hartwig singularities.