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More specifically, how do you define the square root of an $n\times n$ matrix A and express it in linear algebra terms? Does this have something to do with positive semi-definite matrices and diagonalization?

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    I think this wiki article should do the deal: http://en.wikipedia.org/wiki/Square_root_of_a_matrix2011-12-21
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    Related posts: http://math.stackexchange.com/questions/57292/for-every-matrix-a-in-m-2-mathbbc-theres-x-in-m-2-mathbbc-s, http://math.stackexchange.com/questions/65227/square-root-of-a-matrix, http://math.stackexchange.com/questions/72551/a-question-about-n-times-n-matrix2011-12-21

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