An order bounded disjointness preserving operator T on an Archimedean vector lattice is algebraic if and only if the restriction of Tn! to the vector sublattice generated by the range of Tm is strongly diagonal, where n is the degree of the minimal polynomial of T and m is its ‘valuation’.

Let L/K be a separable field extension of degree 6. An 1867 theorem of P. Joubert asserts that if char(K) 6= 2 then L is generated over K by an element whose minimal polynomial is of the form t + at + bt + ct+ d for some a, b, c, d ∈ K. We show that this theorem fails in

This lecture introduces the Jordan canonical form of a matrix — we prove that every square matrix is equivalent to a (essentially) unique Jordan matrix and we give a method to derive the latter. We also introduce the notion of minimal polynomial and we point out how to obtain it from the Jordan canonical form. Finally, we make an encounter with companion matrices. 1 Jordan form and an applicati...

In [4] the authors proposed a collocation algorithm for approximating the minimal norm least-squares solution of first kind integral equations with continuous reproducing kernel. The convergence of the approximate solutions sequence is proved under the assumption that all the sets of collocation functions are linearly independent. In this paper we replace the above assumption by a weaker one an...