Search results for "subspace"
showing 4 items of 164 documents
Polaroid-Type Operators
2018
In this chapter we introduce the classes of polaroid-type operators, i.e., those operators T ∈ L(X) for which the isolated points of the spectrum σ(T) are poles of the resolvent, or the isolated points of the approximate point spectrum σap(T) are left poles of the resolvent. We also consider the class of all hereditarily polaroid operators, i.e., those operators T ∈ L(X) for which all the restrictions to closed invariant subspaces are polaroid. The class of polaroid operators, as well as the class of hereditarily polaroid operators, is very large. We shall see that every generalized scalar operator is hereditarily polaroid, and this implies that many classes of operators acting on Hilbert s…
Determining the number of sources in high-density EEG recordings of event-related potentials by model order selection
2011
To high-density electroencephalography (EEG) recordings, determining the number of sources to separate the signal and the noise subspace is very important. A mostly used criterion is that percentage of variance of raw data explained by the selected principal components composing the signal space should be over 90%. Recently, a model order selection method named as GAP has been proposed. We investigated the two methods by performing independent component analysis (ICA) on the estimated signal subspace, assuming the number of selected principal components composing the signal subspace is equal to the number of sources of brain activities. Through examining wavelet-filtered EEG recordings (128…
Students' problems in the identification of subspaces in Linear Algebra
2018
International audience; The goal of the study presented in this paper is the investigation of students' problems with exercises concerning central topics of linear algebra courses at university level. We present the results of our analysis of students' work on an exercise about subspaces of . We evaluated the written solutions of the task as well as transcripts based on videos taken of student groups working on the problem. We identified and classified descriptions of vector spaces and subspaces that varied widely and demonstrated highly different skills in working with geometric or formal algebraic objects. We analyzed how far students could progress in a complex reasoning process, and ide…
Dynamics of a harmonic oscillator coupled with a Glauber amplifier
2020
A system of a quantum harmonic oscillator bi-linearly coupled with a Glauber amplifier is analysed considering a time-dependent Hamiltonian model. The Hilbert space of this system may be exactly subdivided into invariant finite dimensional subspaces. Resorting to the Jordan-Schwinger map, the dynamical problem within each invariant subspace may be traced back to an effective SU(2) Hamiltonian model expressed in terms of spin variables only. This circumstance allows to analytically solve the dynamical problem and thus to study the exact dynamics of the oscillator-amplifier system under specific time-dependent scenarios. Peculiar physical effects are brought to light by comparing the dynamics…