Related papers: Matrices with invariant by rotation numerical rang…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
A minimal homogeneous generating system of the algebra of semi-invariants of tuples of two-by-two matrices over an infinite field of characteristic two or over the ring of integers is given. In an alternative interpretation this yields a…
We construct an open set of endomorphisms of an arbitrary two-dimensional manifold which have attractors and non-wandering sets with non-invariant interior. This is a notable contrast to the properties of diffeomorphisms, where the interior…
By definition, reciprocal matrices are tridiagonal $n$-by-$n$ matrices $A$ with constant main diagonal and such that $a_{i,i+1}a_{i+1,i}=1$ for $i=1,\ldots,n-1$. For $n\leq 6$, we establish criteria under which the numerical range…
Criterion for a companion matrix to have a certain number of flat portions on the boundary of its numerical range is given. The criterion is specialized to the cases of 3-by-3 and 4-by-4 matrices. In the latter case, it is proved that a…
Let X be a smooth complex variety and Y be a closed subvariety of X, or more generally, a closed subscheme of X. We are interested in invariants attached to the singularities of the pair (X, Y). We discuss various methods to construct such…
Two of many criteria of a good MDS matrix are being involutory and having few different elements. This paper investigates the number of different entries in an involutory MDS matrices of order 1, 2, 3, and 4 over finite fields of…
We present a construction of new invariant sets for fibred polynomial dynamics with base an irrational rotation over the unit circle, called multi-curves. Furthermore, the local dynamical theory for attracting invariant curves is extended…
Identity-homotopic self-homeomorphisms of a space of non-periodic 1-dimensional tiling are generalizations of orientation-preserving self-homeomorphisms of circles. We define the analogue of rotation numbers for such maps. In constrast to…
We study the differential geometric properties of the manifold of non-singular symmetric real matrices endowed with the trace metric; in case of positive definite matrices we describe the full group of isometries
We comment two papers of Domokos and Vaccarino proving that the restriction to diagonal matrices of the scheme of commuting matrices is an isomorphism when restricted to invariants to the symmetric group invariants.
Why is it that after so many years matrices continue to play such an important roll in Physics and mathematics? Is there a geometric way of looking at matrices, and linear transformations in general, that lies at the roots of their success?…
We prove some eigenvalue inequalities for positive semidefinite matrices partitioned into four blocks. The inradius of the numerical range of the off-diagonal block contributes to these estimates. Some related norm inequalities are given…
This article presents and compares four approaches for computing the rotation of a point about an axis by an angle in $\mathbb{R}^3$. We illustrate these methods by computing, by hand, the rotation of point $P=(1,0,1)^T$ about axis…
The f-invariant is a higher version of the e-invariant that takes values in the divided congruences between modular forms; it can be formulated as an elliptic genus of manifolds with corners of codimension two. In this thesis, we develop a…
Several new verifiable conditions are established for block matrices with scalar diagonal blocks to have the numerical range equal the convex hull of at most k ellipses where k by k is the size of the smaller diagonal block. For k = 2,…
We consider the existence of invariant curves of real analytic reversible mappings which are quasi-periodic in the angle variables. By the normal form theorem, we prove that under some assumptions, the original mapping is changed into its…
The positive stability and D-stability of singular M-matrices, perturbed by (non-trivial) nonnegative rank one perturbations, is investigated. In special cases positive stability or D-stability can be established. In full generality this is…
An invariant of a model of genus one curve is a polynomial in the coefficients of the model that is stable under certain linear transformations. The classical example of an invariant is the discriminant, which characterizes the singularity…
Orthogonal Mueller matrices can be considered either as corresponding to retarders or to generalized transformations of the polarization basis for the representation of Stokes vectors, so that they constitute the only type of Mueller…