Practice question · Multiple choice
Two phone carriers trade customers monthly by a fixed transition matrix. Whatever the starting split, shares always drift to 60/40 and stay. In eigen-language, is…
Hints
- Steady means: multiplied by the matrix, unchanged.
- .
Show the answer
C. The eigenvector of eigenvalue 1
Why
"Drifts there and stays" is precisely : eigenvalue 1, eigenvector = the long-run market share. The drift from any start is the dominant eigenvector asserting itself over the fading ones.
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