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Basic Definitions 1. 2. 3. 4. Positive Matrix: 5. Non-negative Matrix:

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Page 1: Basic Definitions 1. 2. 3. 4.Positive Matrix: 5.Non-negative Matrix:

Basic Definitions

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4. Positive Matrix:

5. Non-negative Matrix:

Page 2: Basic Definitions 1. 2. 3. 4.Positive Matrix: 5.Non-negative Matrix:

Perron Theorem for Positive Matrices

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Page 3: Basic Definitions 1. 2. 3. 4.Positive Matrix: 5.Non-negative Matrix:

Non-Negative Matrices

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Irreducibility

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Corresponding Graph of a Matrix

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Page 6: Basic Definitions 1. 2. 3. 4.Positive Matrix: 5.Non-negative Matrix:

More on Irreducibility

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Page 7: Basic Definitions 1. 2. 3. 4.Positive Matrix: 5.Non-negative Matrix:

Perron-Frobenius Theorem I

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Perron-Frobenius Theorem II

Page 9: Basic Definitions 1. 2. 3. 4.Positive Matrix: 5.Non-negative Matrix:

Primitive Matrices I

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Primitive Matrices II

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Page 11: Basic Definitions 1. 2. 3. 4.Positive Matrix: 5.Non-negative Matrix:

Stochastic Matrices

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Page 12: Basic Definitions 1. 2. 3. 4.Positive Matrix: 5.Non-negative Matrix:

Markov Chains I (Definitions)

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Markov Chains II (States)

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Page 14: Basic Definitions 1. 2. 3. 4.Positive Matrix: 5.Non-negative Matrix:

Markov Chains III (Classes)

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Page 15: Basic Definitions 1. 2. 3. 4.Positive Matrix: 5.Non-negative Matrix:

Markov Chains IV (Matrices)

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Page 16: Basic Definitions 1. 2. 3. 4.Positive Matrix: 5.Non-negative Matrix:

Markov Chains V (Stationary Distribution and Long-Run Behavior)

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