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Propositions from Markov systems

All propositions from Markov systems.

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[PROPOSITION]

Probability vectors remain probability vectors

If $\mathbf{x}$ has non-negative entries summing to $1$ and $A$ is a transition matrix, then $A\mathbf{x}$ also has non-negative entries summing to $1$ .

[1]:Transition matrix
[2]:Markov system
[3]:Proof
[4]:A three-state stock market

This page builds on Eigenvalues and eigenvectors, Spectral applications, Matrix representations (Linear transformations) and Diagonalisation.

It leads to Seen Questions.

Part of the thread Roots, modes and evolution, in 7 places.

A linear evolution splits into modes $r^n$ or $e^{rt}$ , and the roots $r$ decide growth, decay and oscillation.

ALGCAL124

THA sufficient condition for long-term Markov behaviourMarkov systemsALG 4 / Here

Propositions from Markov systems

Probability vectors remain probability vectors

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