In linear algebra, the \'Cayley-Hamilton theorem' (named after the mathematicians Arthur Cayley and William Hamilton) states that every square matrix over a commutative ring, e.g. over the real or complex field, satisfies its own characteristic equation. This means the following: if A is the given square matrix and
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As a result of this, the Cayley-Hamilton theorem allows us to calculate powers of matrices more simply than by direct multiplication.
Taking the result above