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Instituto Federal de Educação, Ciência e Tecnologia de São Paulo (IFSP). Campus São José dos Campos (Institutional affiliation from the last research proposal) Birthplace: Brazil
Mathematician with a Ph.D. in Physics and Astronomy. Holds expertise in Algebra, Topology, Dynamical Systems, and Chaos. He is a full-time professor and researcher at the Faculty of Mathematics at the Federal Institute of Education, Science, and Technology of São Paulo (IFSP) on the São José dos Campos - Petrobrás campus. Currently, he serves as the coordinator of Research, Innovation, and Postgraduate Studies at the institution. From August 2020 to August 2022, he was the coordinator of the Mathematics Teaching program at IFSP. He has authored two books, "Geometria e Trigonometria Esférica: Fundamentos e Aplicações" and "Tópicos Selecionados em Estruturas Algébricas," set to be released in early 2024 by Ciência Moderna Publisher. (Source: Lattes Curriculum)
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The Fibonacci sequence $(F_n)$ and the Lucas sequence $(L_n)$ have a deep connection with certain matrices known as $Q$-matrices. The Fibonacci $Q$-matrix, $Q_F = \begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix}$, is known for the fact that its $n$-th power satisfies$Q_F^n = \begin{bmatrix} F_{n+1} & F_n \\ F_n & F_{n-1} \end{bmatrix}$. Similarly, the Lucas $Q$-matrix, $Q_L = \begin{bmatrix}…
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