We consider ecological difference equations of the form xt+1 = x i tAi(xt), where x i t is a vector of densities corresponding to the subpopulations of species i (e.g., subpopulations of different ages or living in different patches), xt = (xt , x 2 t , . . . , x m t ) is the state of the entire community, and Ai(xt) are matrices determining the update rule for species i. These equations are pe...

I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with the trace of an odd product of gamma matrices in odd dimensions. The regularization is completed with an evanescent higher-derivative deformation, which proves...

Over the past few years, symmetric positive definite matrices (SPD) have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the two most widely-used measures are affine-invariant distance and log-Euclidean distance. This is because these two measures are true geodesic distances induced...

The notions of input and output decoupling zeros are extended to a linear periodic discretetime system. The ordered sets of structural indices are also analyzed for these notions and for the notions of invariant zero, transmission zero, eigenvalue and pole of such a system. For any non-zero zero, eigenvalue and pole, the corresponding ordered set of structural indices is timeinvariant. The inpu...

The existence and construction of common invariant cones for families of real matrices is considered. The complete results are obtained for 2× 2 matrices (with no additional restrictions) and for families of simultaneously diagonalizable matrices of any size. Families of matrices with a shared dominant eigenvector are considered under some additional conditions.

The paper considers parametric uncertain systems of the form ẋ t Mx t ,M ∈ M,M ⊂ Rn×n, where M is either a convex hull, or a positive cone of matrices, generated by the set of vertices V {M1,M2, . . . ,MK} ⊂ Rn×n. Denote by μ‖ ‖ the matrix measure corresponding to a vector norm ‖ ‖. When M is a convex hull, the condition μ‖ ‖ Mk ≤ r < 0, 1 ≤ k ≤ K, is necessary and sufficient for the existence ...

In this paper we study Jordan-structure-preserving perturbations of matrices selfadjoint in the indefinite inner product. The main result of the paper is Lipschitz stability of the corresponding similitude matrices. The result can be reformulated as Lipschitz stability, under small perturbations, of canonical Jordan bases (i.e., eigenvectors and generalized eigenvectors enjoying a certain flipp...

A brief but concise review of methods to generate P-matrices (i.e., matrices having positive principal minors) is provided and motivated by open problems on P-matrices and the desire to develop and test efficient methods for the detection of P-matrices. Also discussed are operations that leave the class of P-matrices invariant. Some new results and extensions of results regarding P-matrices are...

Invariant subspaces of structured matrices are sometimes better conditioned with respect to structured perturbations than with respect to general perturbations. Sometimes they are not. This paper proposes an appropriate condition number cS, for invariant subspaces subject to structured perturbations. Several examples compare cS with the unstructured condition number. The examples include block ...

Invariant Coordinate Selection (ICS) is a multivariate data transformation and dimension reduction method that can be useful in many different contexts. It used for outlier detection or cluster identification, seen as an independent component non-Gaussian analysis method. The usual implementation of ICS based on joint diagonalization two scatter matrices, may numerically unstable some ill-condi...