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See also: Matrix Inversion |
A matrix A is called a stochastic matrix, if it does not contain any negative entries and the sum of each row of the matrix is equal to 1.0. The product of two stochastic matrices is again a stochastic matrix. Therefore, one can deduct that all powers of stochastic matrices A^{n} are stochastic matrices.
A special case of a stochastic matrix is the regular matrix. A stochastic matrix A is said to be regular if all elements of at least one particular power of A are positive and different from zero. Regular matrices are important for the calculation of probabilities of dependant processes (Markov chains). For a regular matrix always an inverse matrix exists, which fulfills the following equation: A A^{-1} = A ^{-1} A = I.
Last Update: 2002-Nov-03