A matrix equation $X^n = aI$

preprint2014arXivOpen access

In this paper, we study a matrix equation $X^n = aI$ . We factorize $X^n - aI$ based upon the factorization of $x^n - a$ and then give a necessary and sufficient condition for one of the factors to be the zero matrix.

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A matrix equation $X^n = aI$

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A matrix equation Xn=aIX^n = aIXn=aI

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A matrix equation $X^n = aI$