Efficient computation of enclosures for the exact solvents of a quadratic matrix equation.
Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.
Estimation of the noncentrality matrix of a noncentral Wishart distribution with unit scale matrix. A matrix generalization of Leung's domination result.
The main aim is to estimate the noncentrality matrix of a noncentral Wishart distribution. The method used is Leung's but generalized to a matrix loss function. Parallelly Leung's scalar noncentral Wishart identity is generalized to become a matrix identity. The concept of Löwner partial ordering of symmetric matrices is used.
Explicit forms of block matrices in unbalanced cross classification
Explicit inverse of an interval matrix with unit midpoint.
Explicit Solutions of some Linear Matrix Equations
Extremal inverse eigenvalue problem for matrices described by a connected unicyclic graph
In this paper, we deal with the construction of symmetric matrix whose corresponding graph is connected and unicyclic using some pre-assigned spectral data. Spectral data for the problem consist of the smallest and the largest eigenvalues of each leading principal submatrices. Inverse eigenvalue problem (IEP) with this set of spectral data is generally known as the extremal IEP. We use a standard scheme of labeling the vertices of the graph, which helps in getting a simple relation between the characteristic...
Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation.