Consider $T = (x_1,..,x_5) \to (x_4, x_5)$. We have $\operatorname{null} T = \{(x_1,x_2,x_3,0,0) | x_1,x_2,x_3 \in \mathbb{F}\}$, and $\operatorname{range} T ...

(ST)(T^{-1}S^{-1}) = STT^{-1}S^{-1} = SS^{-1} = I Hence, $ST$ is invertible and $(ST)^{-1} = T^{-1}S^{-1}$. _Exercise 2_ Let $N$ be the set of noninvertible operators ...

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, ...

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 ...

We show that every unital linear bijection which preserves the maximal left ideals from a semi-simple Banach algebra onto a C *-algebra of real rank zero is a Jordan isomorphism. Furthermore, every ...

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 ...

*Note: This course discription is only applicable to the Computer Science Post-Baccalaureate program. Additionally, students must always refer to course syllabus for the most up to date information.

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 ...