Complementable and almost definite matrices

Definite and Quasidefinite Sets of Stochastic Matrices'

Solitons and almost-intertwining matrices

We define the algebraic variety of almost intertwining matrices to be the set of triples ~X,Y,Z! of n3n matrices for which XZ5YX1T for a rank one matrix T. A surprisingly simple formula is given for tau functions of the KP hierarchy in terms of such triples. The tau functions produced in this way include the soliton and vanishing rational solutions. The induced dynamics of the eigenvalues of th...

Almost-commuting matrices are almost jointly diagonalizable

We study the relation between approximate joint diagonalization of self-adjoint matrices and the norm of their commutator, and show that almost commuting self-adjoint matrices are almost jointly diagonalizable by a unitary matrix.

Embedding nonnegative definite Toeplitz matrices in nonnegative definite circulant matrices, with application to covariance estimation

Ahtract -The class of nonnegative definite Toeplitz matrices that can be embedded in nonnegative definite circulant matrices of larger sue is characterized. An equivalent characterization in terms of the spectrum of the underlying process is also presented, together with the corresponding extrema1 processes. It is shown that a given finite duration sequence p can be extended to be the covarianc...

Almost Separable Matrices

An m × n matrix A with column supports {Si} is k-separable if the disjunctions ⋃ i∈K Si are all distinct over all sets K of cardinality k. While a simple counting bound shows that m > k log2 n/k rows are required for a separable matrix to exist, in fact it is necessary for m to be about a factor of k more than this. In this paper, we consider a weaker definition of ‘almost k-separability’, whic...