During my second course in linear algebra, I encountered a frequent need to convert linear maps into matrices. This task became particularly challenging when working with complex maps and bases, ...

1 Department of Mathematical Sciences, Mathematical Finance and Econometrics, Catholic University of the Sacred Heart, Milan, Italy 2 Department of Economics, University of Bamberg, Bamberg, Germany ...

Linear maps are abstractly defined things. We’d like to make them concrete. We do this by making the following observation: once you know what a linear transformation does on a basis, you know what it ...

Verification of large programs is impossible without proof techniques that allow local reasoning and information hiding. In this paper, we resurrect, extend and modernize an old approach to this ...

But an arbitrary function between two vector spaces doesn’t necessarily give you any information about their relationship as vector spaces. To get such information, we need to restrict to functions ...

Let 𝓤 be a unital ★-algebra and δ : 𝓤 → 𝓤 be a linear map behaving like a derivation or an anti-derivation at the following orthogonality conditions on elements of 𝓤: xy = 0, xy★ = 0, xy = yx = 0 ...