In this thesis we are concerned with themes suggested by rank properties of subspaces of matrices. Historically, most work on these topics has been devoted to matrices over such fields as the real or complex numbers, where geometric or analytic methods may be applied. Such techniques are not obviously applicable to finite fields, and there were very few general theorems relating to rank problem...

Identification of mixed independent subspaces is thought to suffer from combinatorial explosion of two kinds: the minimization of mutual information between the estimated subspaces and the search for the optimal number and dimensions of the subspaces. Here we show that independent auto-regressive process analysis, under certain conditions, can avoid this problem using a two-phase estimation pro...

The wavelet subspaces of the space of square integrable functions on the affine group with respect to the left invariant Haar measure dν are studied using the techniques from [9] with respect to wavelets whose Fourier transforms are related to Laguerre polynomials. The orthogonal projections onto each of these wavelet subspaces are described and explicit forms of reproducing kernels are establi...

‎Let $G$ be a locally compact abelian group‎. ‎The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$‎. ‎Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level‎. ‎Also‎, ‎the construction of affine frames for $L^2(G)$ bas...

This paper introduces a subspace segmentation and data clustering method for a set of data drawn from a union of subspaces. The proposed method works perfectly in absence of noise, i.e., it can find the number of subspaces, their dimensions, and an orthonormal basis for each subspace. The effect of noise on this approach depends on the noise level and relative positions of subspaces. We provide...

We formulate the problem of tracking principal subspaces as a problem in nonlinear ltering. The subspaces are represented by their complex projection-matrices, and moving subspaces correspond to trajectories on the Grassmann man-ifold. Taking a Bayesian approach, we impose a smoothness prior on the subspace rotation. Combining ideas from importance sampling and sequential methods, we apply a re...

In this contribution lossy image compression based on subspaces clustering is considered. Given a PCA factorization of each cluster into subspaces and a maximal compression error, we show that the selection of those subspaces that provide the optimal lossy image compression is equivalent to the 0-1 Knapsack Problem. We present a theoretical and an experimental comparison between accurate and ap...

In this paper, we investigate several theoretical and computational aspects of fundamental subspaces for linear, time-invariant (LTI) descriptor systems, which appear in the solution of many control and estimation problems. Different types of reachability and controllability for descriptor systems are described and discussed. The Rosenbrock system matrix pencil is employed for the computation o...

The aim of this note is to extend the notion of invariant subspaces known in the geometric control theory of the linear time invariant systems to the linear parameter-varying (LPV) systems by introducing the concept of parameter-varying invariant subspaces. For LPV systems affine in their parameters, algorithms are given to compute many parameter varying subspaces relevant in the solution of st...

Null designs on the poset of dual polar spaces are considered. A poset of dual polar spaces is the set of isotropic subspaces of a finite vector space equipped with a nondegenerate bilinear form, ordered by inclusion. We show that the minimum number of isotropic subspaces to construct a nonzero null t-design is Qt i=0(1 + q ) for the types BN , DN , whereas for the case of type CN , more isotro...