The eigenvalues and eigenvectors experiment explores fundamental linear transformation principles in mathematics, revealing how matrices modify vector characteristics. When a matrix transforms a vector, an eigenvector maintains its original directional orientation, while the corresponding eigenvalue represents the scaling factor of this transformation. This computational process involves solving complex mathematical equations to determine unique scalar values (eigenvalues) and their associated vectors that remain parallel during matrix multiplication. By utilizing numeric computational methods, the experiment enables users to interactively generate matrices between 2x2 and 10x10, dynamically calculate eigenvalues and eigenvectors, and visually understand how linear transformations impact geometric representations. The significance of this mathematical exploration extends across diverse fields including physics, engineering, computer graphics, and machine learning, where understanding matrix transformations provides critical insights into system behaviors, dimensional reductions, and structural analyses. Through an intuitive interface allowing real-time slider-based matrix configuration, the experiment bridges abstract mathematical concepts with practical, interactive learning, demonstrating how seemingly complex linear algebraic principles can be explored and comprehended through systematic computational techniques.