Another method to obtain Pythagorean Triple Preserving Matrices is proposed and a singular case is put in evidence. Also, a possible connection with physics is sketched by proving that the set of these matrices is a group. In the last section, we generalize our method to Weighted Pythagorean Triple Preserving Matrices. An interesting open problem is generated by the fact that this type of matrix appears as a product of two matrices of order 4 with a form suggesting quaternions.

By creating a geometric interpretation for $2 \times 2$ Markov chain transition matrices, we obtain a simple graphical method for finding the limiting probability vector. As a bonus, the interpretation gives a geometric method for finding powers and roots of transition matrices.

Procedures for detecting a changepoint in a sequence of $N$ random $p$-vectors, when there is a location or a scale change are considered. An extension of such procedures for the case of simultaneous occurrence of location and scale changes is carried out. The asymptotic distributions of the proposed statistics under the null hypothesis, in two different changepoint models are obtained.

In this paper, solutions of two old problems of D. Ž. Djoković are given. One solution of the first problem is given by O. P. Lossers [2] in implicit form and the other solution by another method is given in explicit form. The second problem is solved here for the first time.