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, ...
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 ...
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 ...
(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 ...
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 ...
Abstract: Chaotic signals generated by iterating piecewise-linear (PWL) maps on the unit interval are highly attractive in a wide range of signal processing applications. In this letter, optimal ...
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