The aim of this thesis is to explain by using linear algebra, the calculation of one of the most commonly used mathematical-statistical methods for reducing the dimensionality of large datasets of present-day science and practice - factor analysis. In accordance with the objective, the matrix algebra of the factor analysis calculations is presented, and the rotation of the factors, given the complexity of the problem, is numerically demonstrated only for a given angle. It has been emphasized that, as opposed to orthogonal rotations, oblique rotations allow the determination of higher order factors, thus becoming more utilitarian in scientific practice. Despite the lack of complete consensus in the science of the use and application of rotation types for professional and scientific practice, especially in the maritime and related sciences, it is emphasized that the existence of interdependent relationships among extracted latent constructs - factors. The computational operations of matrix algebra in this paper offered one of a possible solutions to rotations, and in accordance with the aim of the paper, pointed out the necessity of rotation of the initial matrix of the principal axes. The results of this paper can serve to gain a deeper insight into the problem of the application of factor analysis in the maritime and related sciences.