Status: Tags: #cards/math232/unit6 Links: Diagonalization
Applications of Diagonalization
Principles
Powers of Matrices
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Markov Processes
General info ?
- Markov Chain, mathematical model of a system that occupies one of a finite number of states, and how the system transitions to the next state is dependent only on its current state
- Used in:
- Chemical reactions
- Population genetics
- Random walks
Textbook definition
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Fixed state vector ?
- Eigenvector for the eigenvalue = 1
- Minus it from the diagonal and RREF to find nullspace
- $λI - P$, should lead to same absolute values for each col
Find invariant state ?
- Make the column/vector = 1
Differential Equations
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- Entering and leaving at a constant rate
Solving
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Examples
Powers of Matrices
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markov
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diff equations
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References:
Created:: 2022-03-16 19:05