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 ...

Algebraic structures and linear maps form a cornerstone in modern mathematics, underpinning areas as diverse as abstract algebra and functional analysis. Algebraic structures such as groups, rings, ...

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 ...

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 ...

Abstract: Linear map commitments allow the prover to commit to a vector, with the ability to prove the image of a linear map acting on the vector. In this paper, we propose linear map commitments with ...

A new mathematical framework outlining an invertible linear transformation matrix that maps points from one abstract geometric space onto another, while preserving the underlying topology and ...