On congruent circulant matrices
Abstract
In this work, we investigate congruent circulant matrices and provide a parametrization of congruent matrices in M2(Q ). We introduce a matrix analogue of Fermat’s algorithm, which enables the construction of sequences of matrix Pythagorean triples associated with a given 2 2 congruent circulant matrix N. Furthermore, we establish a matrix version of Pythagoras’ theorem within the Euclidean vector space Mm(Q ); m >= 2.
Mathematics Subject Classification (MSC2020). 11C20, 15A15, 15A18, 15A20,
15A27, 15A60, 11D72.
https://doi.org/10.70974/mat09125086
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