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@@ -28,8 +28,6 @@ In addition to what's in Anaconda, this lecture will need the following librarie

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!pip install quantecon

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```

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In this lecture we will begin with the foundational concepts in spectral theory.

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Then we will explore the Perron-Frobenius Theorem and connect it to applications in Markov chains and networks.

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We will use the following imports:

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A primitive matrix is both irreducible and aperiodic.

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So Perron-Frobenius Theorem explains why both Imam and Temple matrix and [Hamilton matrix](https://en.wikipedia.org/wiki/Hamiltonian_matrix) converge to a stationary distribution, which is the Perron projection of the two matrices

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So Perron-Frobenius Theorem explains why both {ref}`Imam and Temple matrix <mc_eg3>` and [Hamilton matrix](https://en.wikipedia.org/wiki/Hamiltonian_matrix) converge to a stationary distribution, which is the Perron projection of the two matrices

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```{code-cell} ipython3

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P = np.array([[0.68, 0.12, 0.20],

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