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 us denote $u_1,...,u_n$ to be canonical basis of $\mathbb{F}^n$, i.e. $u_1 = (1,0,...,0)$, ..., $u_n = (0,0,...,1)$. We can define $T$ fully by defining its ...

An s-entanglement breaking map between operator systems is a point-norm limit of entanglement breaking maps, which are a generalization of the corresponding notion in matrix algebras. We develop some ...

which holds purely because composing with an identity map doesn’t change anything. Now apply Theorem 4.19.1 from the previous section twice: you get the change of basis formula: In this subsection ...

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 ...

The aim of this paper is to show that there are no piecewise linear maps of type 2∞. For this purpose we use the fact that any piecewise monotone map of type 2∞ has an infinite ω-limit set which is a ...

Transfer matrix methods are widely used to calculate properties of particle orbits as they pass through linear beam elements such as drif t spaces, bending magnets, and quadrupoles. A new method of ...