The thesis focuses on powers of positive matrices. They are closely related to eigenvalues and eigenvectors of said matrices. For this reason the thesis explains the procedure for calculating eigenpairs and their characteristics. On the basis of Jordan normal form the thesis explains a simpler way of calculating powers of matrices and also other matrix functions. It also explains the characteristics of powers of stochastic or probability matrices. The centre theorems of this thesis are Perron-Frobenius and Perron theorem. The first focuses on characteristics of positive matrices, which then the second uses to compute limits of sequences of powers of positive matrices. Everything we learn is then used in examples from real life, where we can see the usefulness of powers of positive matrices and the reason we started studying them in the first place.
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