In this work we will investigate the generating matrices for the positive integers of the Leonardo sequence, as well as some inherent properties of these matrices. In order to perform the process of generalizing the matrix form of Leonardo’s numbers, the extension to the field of non-positive integers is performed, in which the study of these matrices is unpublished in this research. The matrix form relates the matrices to the Leonardo numbers, and by raising these matrices to nth power, we obtain some new relations of this sequence, thus knowing their respective terms.
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Vieira et al. (2020) studied this question.