Each person’s unique traits hold valuable insights into their consumer behavior, allowing scholars and industry experts to develop innovative marketing strategies, personalized solutions, and enhanced user experiences. This study presents a conceptual framework that explores the connection between fundamental personality dimensions and users’ online shopping styles. By employing the TIPI test, a reliable and validated alternative to the Five-Factor model, individual consumer profiles are established. The results reveal a significant relationship between key personality traits and specific online shopping functionalities. To accurately forecast customers’ needs, expectations, and preferences on the Internet, we propose the implementation of two Machine Learning models, namely Decision Trees and Random Forest. According to the applied evaluation metrics, both models demonstrate fine predictions of consumer behavior based on their personality.

A rigorous perturbation analysis is presented for the singular value decomposition (SVD) of a real matrix with full column rank. It is proved that the SVD perturbation problem is well posed only when the singular values are distinct. The analysis involves the solution of symmetric coupled systems of linear equations. It produces asymptotic (local) componentwise perturbation bounds on the entries of the orthogonal matrices participating in the decomposition of the given matrix and on its singular values. Local bounds are derived for the sensitivity of the singular subspaces measured by the angles between the unperturbed and perturbed subspaces. Determining the asymptotic bounds of the orthogonal matrices and the sensitivity of singular subspaces requires knowing only the norm of the perturbation of the given matrix. An iterative scheme is described to find global bounds on the respective perturbations, and results from numerical experiments are presented.

The study aims to examine the issue of the relationship between Emotional stability, one of the fundamental personality determinants, and users’ Risk Averseness, on the one hand, and user behavior in the field of e-Commerce, on the other hand. In the beginning, a brief overview of today’s primary benchmark for the measurement of human personality – the Big Five Model is proposed. A study with 226 participants has been conducted for the aim of the research, based on the TIPI test. The TIPI test is a validated and abridged version of the Five-Factor model. The result of the conducted survey confirms the existence of significant relationships between personality determinant Emotional stability and consumer’s Risk awareness, on one side, and some of the observed main functionalities of the online stores, on the other side. Two regression models of the field of Machine Learning (Linear Regression and Random Forest) have been implemented to make a reliable forecast about the user’s preferences in the process of online shopping. The conclusions made rely on the obtained results and analysis.

Nonsymmetric differential matrix Riccati equations arise in many problems related to science and engineering. This work is focusing on the sensitivity of the solution to perturbations in the matrix coefficients and the initial condition. Two approaches of nonlocal perturbation analysis of the symmetric differential Riccati equation are extended to the nonsymmetric case. Applying the techniques of Fréchet derivatives, Lyapunov majorants and fixed-point principle, two perturbation bounds are derived: the first one is based on the integral form of the solution and the second one considers the equivalent solution to the initial value problem of the associated differential system. The first bound is derived for the nonsymmetric differential Riccati equation in its general form. The perturbation bound based on the sensitivity analysis of the associated linear differential system is formulated for the low-dimensional approximate solution to the large-scale nonsymmetric differential Riccati equation. The two bounds exploit the existing sensitivity estimates for the matrix exponential and are alternative.