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...rans_matrix)$vectors # create a diagonalized matrix of the eigenvalues of the transition matrix L <- diag(eigen(trans_matrix)$values) # calculate inverse of matrix of eigenvectors of the transition matrix X_inv <- solve(X) # calculate the 12th root of the eigenvalues in the diagonal matrix L_star <- L ^ (1/12) # calculate the 12th root of the transition matrix nth_root <- X_inv %*% L_star %*% X ------ END PASTE ------ References: [1] Hull, John. Risk Management and Financial Institutions. Prentice Hall, 2007.