We introduce the notion of analytic stability data on Lie algebra vector fields a torus. prove that subspace is open and closed in topological space all data. formulate general conjecture which explains how give rise to resurgent series. This checked several examples.

0. Introduction. Let H be a complex Hilbert space of finite or infinite dimension, and let E be a collection of bounded linear operators on H. We say E is reducible if there exists a subspace of H, closed by definition and different from the trivial subspaces {0} and H which is invariant under every member of E . We call E triangularizable if the set of invariant subspaces under E contains a ma...

If X is a Banach space such that the isomorphism constant to `2 from n dimensional subspaces grows sufficiently slowly as n → ∞, then X has the approximation property. A consequence of this is that there is a Banach space X with a symmetric basis but not isomorphic to `2 so that all subspaces of X have the approximation property. This answers a problem raised in 1980 [8]. An application of the ...

This paper proposes accelerated subspace optimization methods in the context of image restoration. Subspace optimization methods belong to the class of iterative descent algorithms for unconstrained optimization. At each iteration of such methods, a stepsize vector allowing the best combination of several search directions is computed through a multidimensional search. It is usually obtained by...

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple subspaces through the self-expressiveness property of the data. In particular, the SLRR method considers a collaborative representation combined with low-rank ...

In many scientific applications, including model reduction and image processing, subspaces are used as ansatz spaces for the low-dimensional approximation and reconstruction of the state vectors of interest. We introduce a procedure for adapting an existing subspace based on information from the least-squares problem that underlies the approximation problem of interest such that the associated ...

Subspace methods have emerged as useful tools for the identification of linear time invariant discrete time systems. Most of the methods have been developed for the open loop case to avoid difficulties with data correlations due to the feedback. This paper extends some recent ideas for developing subspace methods that can perform well on data collected both in open and closed loop conditions. H...

Example 3. If X ⊆ RN is a vector space then it is a vector subspace of RN . Example 4. R1 is a vector subspace of R2. But the set [−1, 1] is not a vector subspace because it is not closed under either vector addition or scalar multiplication (for example, 1 + 1 = 2 6∈ [−1, 1]). Geometrically, a vector space in RN looks like a line, plane, or higher dimensional analog thereof, through the origin...

Subspace System Identification is by now an established methodology for experimental modelling. The basic theory is well understood and it is more or less a standard tool in industry. The two main research problems in subspace system identification that have been studied in the recent years are closed loop system identification and performance analysis. The aim of this contribution is quite dif...

Since its very beginning, linear algebra is a highly algorithmic subject. Let us just mention the famous Gauß Algorithm which was invented before the theory of algorithms has been developed. The purpose of this paper is to link linear algebra explicitly to computable analysis, that is the theory of computable real number functions. Especially, we will investigate in which sense the dimension of...