Dispersion Operators Algebra and Linear Canonical Transformations

Canonical forms of Linear Transformations

Linear Algebra: Vector Spaces and Operators

In quantum mechanics the state of a physical system is a vector in a complex vector space. Observables are linear operators, in fact, Hermitian operators acting on this complex vector space. The purpose of this chapter is to learn the basics of vector spaces, the structures that can be built on those spaces, and the operators that act on them. Complex vector spaces are somewhat different from t...

Linear Induction Algebra and a Normal Form for Linear Operators

The set of natural integers is fundamental for at least two reasons: it is the free induction algebra over the empty set (and at such allows definitions of maps by primitive recursion) and it is the free monoid over a one-element set, the latter structure being a consequence of the former. In this contribution, we study the corresponding structure in the linear setting, i.e. in the category of ...

Fine-grained Provenance for Linear Algebra Operators

Provenance is well-understood for relational query operators. Increasingly, however, data analytics is incorporating operations expressed through linear algebra: machine learning operations, network centrality measures, and so on. In this paper, we study provenance information for matrix data and linear algebra operations. Our core technique builds upon provenance for aggregate queries and cons...

Linear Discrete Operators on the Disk Algebra

Let A be the disk algebra. In this paper we address the following question: Under what conditions on the points zk,n ∈ D do there exist operators Ln : A → A such that