Steady State Vector Calculator – Easily Find Your Markov Chain Solutions

Use this tool to calculate the steady state vector of a Markov chain, providing you with the long-term probabilities for each state.

How the Calculator Works

This calculator takes input as a string representation of a square matrix, where the rows are separated by semicolons (;) and the individual numbers by commas (,). It outputs the steady state vector by iteratively updating an initial probability distribution until it converges to a steady state.

How to Use It

Simply input the transition matrix in the specified format, and click “Calculate”. The calculator will display the steady state vector.

How It Calculates Results

This tool iteratively adjusts an initial probability distribution vector. At each step, it computes the new distribution by applying the transition rates from the input matrix. After several iterations, the vector will converge to a steady state, assuming one exists.

Limitations

Due to its iterative nature, the calculator may not converge to the exact steady state vector if the system has no steady state or if it requires more iterations. The input matrix must be square, and this tool is not optimized for very large matrices.

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