Can one take the limit of a matrix as it is multiplied by itself infinite times? We are using a matrix to model how a population changes over a given period of time. Repeated multiplication of the matrix will show how the percentages change after each period of time transpires. The question was will the population stabilize. So I reasoned that if the limit of repeated multiplications of the matrix approached specific values, that the population would indeed stabilize.

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Yes, you can do that. Look up Markov Matrix.

I'll explain.... are you familiar with diagonalization of a matrix?

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