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, ...

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 ...

We introduce the notion of (completely) multi-positive linear maps between C*-algebras, and show that a completely multi-positive linear map induces a representation of a C*-algebra on Hilbert ...

Linear algebra is essential for understanding core data science concepts like machine learning, neural networks, and data transformations. Different books cater to various needs. Some focus on ...