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, ...

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 ...

Let $v_1, \dots, v_m$ denote a basis of $V$. The dimension of $\operatorname{range} T$ is the same as the dimension of $\operatorname{span}(Tv_1, \dots, Tv_m)$. So if ...

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, ...

Abstract: The linear one-turn map of a storage ring contains coupling information on which a correction algorithm can be based. In principal, the one-turn matrix can be fitted from turn-by-turn data ...

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 ...