Matrix generator of pseudorandom numbers (Q1181897)

The authors propose to use the following matrix recurrence as a random number generator: \(P_ N=AP_{N-1}\mod 1\) where \(P_ N\), \(P_{N-1}\) are \(d\)-dimensional vectors and \(A\) is an integer matrix. The paper states that if \(|\text{det }A|\neq 1\) and if all the eigenvalues of \(A\) satisfy the condition \(|\lambda_ i|\neq 1\), \(i=1,2,\dots,d\), then the above generator will have good statistical properties, providing an appropriate choice of \(P_ 0\). A method for constructing the matrix \(A\) is given. The results of a chi-square test for several numerical examples are presented.