Abstract
In this chapter we discuss some of the most important applications of Cayley–Hamilton Theorem which are related to the calculation of powers of square matrices, the computation of the general term of sequences which are defined by systems of linear recurrence relations, the solution of binomial matrix equations, and the study of Pell’s diophantine equation.
The greatest mathematicians like Archimedes,Newton, and Gauss have always been ableto combine theory and applications into one.
Felix Klein (1849–1925)
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- 1.
A fundamental formula for generating Pythagorean triples given an arbitrary pair of positive integers m and n with m > n is Euclid’s formula. The formula states that the integers a = m 2 − n 2, b = 2mn, and c = m 2 + n 2 form a Pythagorean triple [15, p. 165].
- 2.
This equation which bears the name of Pell, due to a confusion originating with Euler, should have been designated as Fermat’s equation [15, p. 341].
- 3.
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Pop, V., Furdui, O. (2017). Applications of Cayley–Hamilton Theorem. In: Square Matrices of Order 2. Springer, Cham. https://doi.org/10.1007/978-3-319-54939-2_3
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DOI: https://doi.org/10.1007/978-3-319-54939-2_3
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