The algebra of quantum matrices of a given size supports a rational torus action by automorphisms. It follows from work of Letzter and the first named author that to understand the prime and primitive spectra of this algebra, the first step is to understand the prime ideals that are invariant under the torus action. In this paper, we prove that a family of quantum minors is the set of all quant...

This brief deals with the asymptotic stability of a class of linear time-invariant systems subject to point constant uncommensurate delays. Results are obtained dependent on and independent of the delays which may be tested be performing a finite set of 1-D Routh–Hurwitz tests on a corresponding set of auxiliary delay-free linear time-invariant systems plus some supplementary conditions related...

Minimizing the Euclidean distance to a set arises frequently in applications. When the set is algebraic, a measure of complexity of this optimization problem is its number of critical points. In this paper we provide a general framework to compute and count the real smooth critical points of a data matrix on an orthogonally invariant set of matrices. The technique relies on “transfer principles...

In the Conley index theory, transition matrices are used to detect bifurcations of codimension one connecting orbits in a Morse decomposition of an isolated invariant set. Here we shall give a new axiomatic definition of the transition matrix in order to treat several existing formulations of transition matrices in a unified manner.

Given the set of matrix pairs M ⊂ Mm,n(C) × Mn(C) keeping a subspace S ⊂ C invariant, we obtain a miniversal deformation of a pair belonging to an open dense subset of M. It generalizes the known results when S is a supplementary subspace of the unobservable one. Keywords-Conditioned invariant subspaces, Miniversal deformation, Stratified manifold, Vertical pairs of matrices.

We find a minimal set of generators for the coordinate ring Calogero-Moser space ${\boldsymbol {\mathcal {C}}}_{\boldsymbol {3}}$ and algebraic relations among them explicitly. give new presentation algebra 3×3 invariant matrices involving defining ${\mathbb {C}}[\boldsymbol {C}}_{\boldsymbol {3}}]$ . Furthermore, we an explicit description GL3-invariant commuting variety its orbits under actio...

For two positive integers m and n, we let Pn be the open convex cone in R consisting of positive definite n × n real symmetric matrices and let R be the set of all m×n real matrices. In this article, we investigate differential operators on the non-reductive manifold Pn × R (m,n) that are invariant under the natural action of the semidirect product group GL(n,R)⋉R on the MinkowskiEuclid space P...

We characterize the exposed faces of convex sets C of symmetric matrices, invariant under orthogonal similarity (U T CU = C for all orthogonal U). Such sets C are exactly those determined by eigenvalue constraints: typical examples are the positive semideenite cone, and unit balls of common matrix norms. The set D of all diagonal matrices in C is known to be convex if and only if C is, and D is...

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

In fermion mixing phenomenology, the matrix of moduli squared, P = (|U |2), is well-known to carry essentially the same information as the complex mixing matrix U itself, but with the advantage of being phase-convention independent. The matrix K (analogous to the Jarlskog CP -invariant J) formed from the real parts of the mixing matrix “plaquette” products is similarly invariant. In this paper,...