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On the Convergence of the Sequence of Powers of a 2 � 2 Matrix

by Roman W. Wong

This article originally appeared in:

January, 2013

Subject classification(s): Stochastic Processes | Probability | Statistics and Probability | Eigenvalues and Eigenvectors | Linear Algebra
Applicable Course(s): 7.3 Stochastic Processes | 3.8 Linear/Matrix Algebra

The fact that the limit of n-th power of a 2\times 2 matrix A tends to 0 if det A < 1 and | 1 + det(A) | > | tr(A) | is used to prove some results for Markov chains.

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