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MENTAL MODEL · M11004

State Transition Matrix

State Transition Matrix
TechnicalHigh supportProbability Theory
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Updated 2026-08-13

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INTRODUCTION

English translation pending.

CORE DEFINITION

A square matrix that encodes the transition probabilities of a Markov chain or the coefficients of a linear state equation. In the probabilistic case each row sums to one, and the entry in row i and column j gives the probability of moving from state i to state j in a single step. The qualification is that the matrix is constant only for time-homogeneous systems; when transition rates change over time it must be re-estimated for each period. Iterated matrix multiplication then yields the distribution over future states.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

- Evolution projection: multiply the current distribution by the matrix to forecast the next period. - Stationary check: iterate the matrix to see where the distribution eventually settles. - Assumption test: verify that the transition probabilities stay stable over the period you are forecasting.

anchor

Anchor fast decisions

Because the next state depends only on the current state, the entire future of the process is compressed into one matrix. Repeated multiplication propagates the distribution forward one step at a time, so long-run behavior such as steady states or absorption probabilities can be read directly from the powers of the matrix rather than simulated case by case.

MINIMUM ACTION

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/State-transition_matrixZH · Explicit
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