👉 The mathematics I'll explain is rooted in linear algebra and its applications, specifically focusing on eigenvalue decomposition. This method is used to simplify complex systems by transforming them into a diagonal form, making it easier to analyze and solve problems involving matrices. Eigenvalues and eigenvectors are key concepts here, representing directions in which a linear transformation acts simply by scaling. This technique is widely applied in various fields, including physics, engineering, and data science, for tasks like stability analysis, principal component analysis, and solving differential equations. By decomposing a matrix into its eigenvalues and eigenvectors, we can gain insights into the behavior of dynamic systems and simplify computations in high-dimensional spaces.
