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I used the Jordan Decomposition, to find such that . Then found the 1000th power of the Jordan form (which was really simple since the Jordan form was an elementary matrix), then remultiplied the corresponding matrices .
Such also factorized really nicely into two elementary matrices which made the final step easier.
Wonder how this method compared to using the Cayley-Hamilton Theorem in terms of speed.
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Linear Algebra Foundations #7 - The 1000th Power of a Matrix
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I used the Jordan Decomposition, to find such that . Then found the 1000th power of the Jordan form (which was really simple since the Jordan form was an elementary matrix), then remultiplied the corresponding matrices . Such also factorized really nicely into two elementary matrices which made the final step easier.
Wonder how this method compared to using the Cayley-Hamilton Theorem in terms of speed.