The spectral radius of the Coxeter transformations for a generalized Cartan matrix.
The spectrum of coupled random matrices.
The Spectrum of Jacobi Matrices.
The Steinitz constant of the plane.
The structure of linear operators strongly preserving majorizations of matrices.
The structure of linear preservers of left matrix majorization on .
The structure of the tame kernels of quadratic number fields (II)
The structured distance to nearly normal matrices.
The structured distance to normality of an irreducible real tridiagonal matrix.
The structured sensitivity of Vandermonde-like systems.
The symmetric linear matrix equation.
The symmetric minimal rank solution of the matrix equation and the optimal approximation.
The symmetric tensor product of a direct sum of locally convex spaces
An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective “full” tensor product of a locally convex space E are isomorphic if E is isomorphic to its square .
The theory and applications of complex matrix scalings
We generalize the theory of positive diagonal scalings of real positive definite matrices to complex diagonal scalings of complex positive definite matrices. A matrix A is a diagonal scaling of a positive definite matrix M if there exists an invertible complex diagonal matrix D such that A = D*MD and where every row and every column of A sums to one. We look at some of the key properties of complex diagonal scalings and we conjecture that every n by n positive definite matrix has at most 2n−1 scalings...
The theory of beta transformation matrices
The third smallest eigenvalue of the Laplacian matrix.
The trace decomposition problem.
The tropical Grassmannian.
The vector cross product from an algebraic point of view
The usual vector cross product of the three-dimensional Euclidian space is considered from an algebraic point of view. It is shown that many proofs, known from analytical geometry, can be distinctly simplified by using the matrix oriented approach. Moreover, by using the concept of generalized matrix inverse, we are able to facilitate the analysis of equations involving vector cross products.
The weak Hawkins-Simon condition.